The question is alluding to the crime of "felony murder".
Historically in England, and in the British colonies, most serious felonies were "capital offenses" punishable by death. But, over time, the scope of crimes eligible for the death penalty was narrowed to murder and a handful of other crimes (e.g. treason and kidnapping where the victim has not been proven to have been released alive, even if the victim's death has not been confirmed), most of which involved a high probability of a homicide, or for a particularly aggravated rape.
The crime of felony murder was invented as one way to further narrow the scope of the death penalty, so that not even all murders were punished by the death penalty. One of the ways this was done was to provide that the death penalty should be available in cases where the murderer was also engaged in the commission of another serious felony named in the statute at the time, and in certain other circumstances showing particular premeditation or depravity, and that other murders should be classified as second degree murders for which a long period of imprisonment should be authorized, but not the death penalty.
Over time, felony murder convictions has become one of the primary and most common bases for a murder conviction to be eligible for the maximum first degree murder punishment, rather than the still very severe second degree murder punishment.
But, somewhere along the way (Wikipedia suggests in 1716, but I would take that with a grain of salt), the concept of felony murder was expanded in many jurisdictions in the U.S. to authorize the death penalty in cases of participation in a conspiracy to commit on of the enumerated felonies which resulted in someone's death, even if the murder itself was not one of the objectives of the conspiracy and the person convicted was not the person who personally killed the person whose murder was being prosecuted.
Often, in states with broad felony murder statutes, the threshold of proof to show that someone was a participant in the underlying felony is also somewhat less rigorous than the standard of proof to show conspiracy, and in many U.S. states, the punishment for conspiracy to commit a crime is not as severe as the punishment for personally committing the crime.
As the "felony murder" link above explains:
As of August 2008, 46 states in the United States had a felony murder
rule, under which felony murder is generally first-degree murder. In
24 of those states, it is a capital offense. When the government seeks
to impose the death penalty on someone convicted of felony murder, the
Eighth Amendment has been interpreted so as to impose additional
limitations on the state power. The death penalty may not be imposed
if the defendant is merely a minor participant and did not actually
kill or intend to kill. However, the death penalty may be imposed if
the defendant is a major participant in the underlying felony and
exhibits extreme indifference to human life.
The major participant/reckless indifference v. minor participant without an intent to kill distinction applies only to the imposition of the death penalty as a punishment for this offense, and not to a conviction for felony murder. Many states (including Colorado) can and do impose a minimum penalty of life in prison without the possibility of parole upon even a minor participant in the conspiracy to commit the statutorily designated felony, who did not intend to kill anyone and did not expect that anyone would be killed.
This expansion of the death penalty (which was upheld as constitutional by the U.S. Supreme Court with the limitations reflected above) reflected the notion that rough justice was appropriate for felons conspiring to commit serious crimes that kill people as severely as possible for any consequences of their collective course of conduct, and that it is more important to punish felons whose engage in activities that kill people than it is to carefully determine which member of a criminal gang actually pulled the trigger.
As a result, it continues to be the case that under the laws of many U.S. states, someone who is a participant in one of the felonies enumerated in the statute committed by multiple people is guilty of first degree murder and often faces a minimum sentence of life in prison without possibility of parole, if anyone is killed in the course of the commission of the felony by any of the participants in the felony, whether or not they had any involvement in the killing itself.
Application To The Facts Presented In The Question
The federal statute is 18 U.S. Code § 1111. This states in the pertinent part that (line breaks and numbering inserted editorially)
(1) Murder is the unlawful killing of a human being with malice
(2) Every murder perpetrated by poison, lying in wait, or any other
kind of willful, deliberate, malicious, and premeditated killing;
(3) or committed in the perpetration of, or attempt to perpetrate, any
arson, escape, murder, kidnapping, treason, espionage, sabotage,
aggravated sexual abuse or sexual abuse, child abuse, burglary, or
(4) or perpetrated as part of a pattern or practice of assault or
torture against a child or children;
(5) or perpetrated from a premeditated design unlawfully and
maliciously to effect the death of any human being other than him who
(6) is murder in the first degree.
(7) Any other murder is murder in the second degree.
There is a solid argument that many of the Capitol rioters were guilty of committing kidnapping or burglary or robbery as discussed at greater length below. But, (1) states that "malice aforethought" must be present in every murder charge under 18 U.S.C. § 1111, and that the person convicted must have committed an "unlawful killing." So, this is even narrower than the D.C. statute discussed below, because every murderer under the federal felony murder statute must have committed a premeditated killing and must have personally participated in the killing.
Thus, under the federal felony murder statute, even people who assaulted the police officer and caused his death, who started their entry into the U.S. Capitol without an intent to kill anyone, would not be guilty of first degree felony murder.
So, if there is such a crime that could have that effect, it would have to be part of the District of Columbia's criminal code.
Does the District of Columbia's felony murder statute have this character?
Or, is it more narrow, simply using participation in the conduct of a felony as an aggravating factor in imposing the maximum sentence upon someone who commits a murder (no District of Columbia criminal code offense carries the death penalty as a punishment, although many federal homicide offenses do)?
To answer that we look at the District of Columbia's felony murder statute (line breaks and numbering inserted editorially for ease of reading and discussion in the Law.SE format):
§ 22–2101. Murder in the first degree — Purposeful killing;
killing while perpetrating certain crimes.
(1) Whoever, being of sound memory and discretion, kills another
(2) purposefully either of deliberate and premeditated malice or by
means of poison, or in perpetrating or attempting to perpetrate an
offense punishable by imprisonment in the penitentiary,
(3) or without purpose to do so kills another in perpetrating or in
attempting to perpetrate any arson, as defined in § 22-301 or §
22-302, first degree sexual abuse, first degree child sexual abuse,
first degree cruelty to children, mayhem, robbery, or kidnaping,
(4) or in perpetrating or attempting to perpetrate any housebreaking
while armed with or using a dangerous weapon,
(5) or in perpetrating or attempting to perpetrate a felony involving
a controlled substance,
(6) is guilty of murder in the first degree. For purposes of
imprisonment following revocation of release authorized by §
24-403.01(b)(7), murder in the first degree is a Class A felony.
So, if element (1) is present, and also element (2) or (3) or (4) or (5), then the defendant is guilty of first degree murder and subject to the punishment set forth in (6).
Since element (1) requires that the defendant "kills another" in addition to an aggravating circumstance set forth in (2), (3), (4) or (5) being present to be guilty of first degree murder, it is apparent that the District of Columbia has a narrower type of felony murder statute that does not impose vicarious criminal liability for murder on participants in felonies that cause deaths who did not themselves kill another, and not the broader type of felony murder statute found in many other U.S. states.
Therefore, it is not the case that all of the many co-conspirators in the January 6, 2021 incident at the U.S. Capitol are exposed to criminal liability for murder, because a police officer was killed in the course of that collective instance of criminal conduct.
This said, everyone who assaulted the police officer who was killed (who died from blows from multiple people) might be guilty of murder, and this could be felony murder even without an intent to kill if the offense or attempted offense was one of the ones identified in (3), (4) or (5) of which three are plausible: mayhem, robbery, or kidnaping.
Mayhem as used in the D.C. felony murder statute appears to refer to assault with intent to create mayhem which has simply its own common meaning of chaotic fear driven chaos, which is a plausible possibility for all of the people who assaulted the police officer.
Robbery generally means theft coupled with the use of force, which would be plausible for a significant number of the participants who stole things from the capitol building in connection with the forceful seizing of control of the capitol building, in addition to participating in the assault of the police officer.
Kidnapping is also plausible in the case of many of the rioters who specifically plotted to hold members of Congress or staffers hostage, even though they were not successful in that attempt, although this is less obvious from the bare events. But if a rioter in the capitol who assaulted the police officer was, for example, carrying zip ties, attempted kidnapping would be very plausible aggravating felony.
What If This Had Happened In A State Capitol Where There Was A Broad Felony Murder Rule?
In contrast, in many U.S. states (for example, Washington State), if the same incidents had unfolded in a state capitol building, all participants in the incident would have been exposed to first degree murder liability.
And, in many states, all major participants who exhibited an indifference to human life would have been exposed to the death penalty, even if they were not the person who actually committed the killing. There is no legal reason that this couldn't implicate dozens or even hundred of participants in the incident.
Also, while the D.C. felony murder statute crimes that might implicate the Capitol protesters are fairly limited to "mayhem, robbery, or kidnaping, or housebreaking while armed with or using a dangerous weapon", one quite common offense in felony murder statutes is "aggravated burglary" which is often defined as trespassing in a building with an intent to commit a crime, while one or the participants is armed with a dangerous weapon, which is an offense that would have included almost all of the D.C. rioters who entered the U.S. capitol building.
N.B. it is also possible for more than one person to be the actual killer in some circumstances, such as this one where the death was caused by the collective effect of blows from multiple individuals.
If this had been the case in a state with a death penalty, it would also have been true that the jury in any such state that had a death penalty would have to be "death qualified" removing all people with moral objections to the death penalty from the jury pool and increasing the likelihood of a conviction on the offense as a result. And, after the jury ruled on guilt or innocence, there would have been a second stage of the trial at which the jury would then consider aggravating and mitigating circumstances presented to it and determine if the sentence should be death or life in prison without the possibility of parole (since automatic death penalty sentences upon conviction for first degree murder are not permitted under U.S. Constitutional law).