"could that guy as defendant claim self defense and win?"
First let's try to make it clear what is meant by "win". In the Rittenhouse trial, the defendant was charged of the following crimes:
- First-degree reckless homicide
- First-degree recklessly endangering safety (x2)
- First-degree intentional homicide
- Attempted first-degree intentional homicide
- Possession of a dangerous weapon by a person under 18 (dismissed)
- Failure to comply with an emergency order from state or local government (dismissed)
Rather than thinking of the defendant as a "winner", it might be more appropriate to say that he was "acquitted" of these charges.
If someone that was involved in the conflict fired first, as you described here:
"They encounter each other when each is leaning or reaching or tripping, or whatever it would take for them to unintentionally point their gun at your head. You react and you raise your gun in defense, he spots your move and points his at you. You both fire. You shoot each other and you both are gravely injured. Like, paralyzed",
then would they also be acquitted of all of the non-dismissed charges listed above? If everything was as you described ("unintentional", "reactionary", and "in defense"), then likely they would also not be found guilty of those crimes. It's not like they would "win", it's more like they will not be found guilty of committing one of those crimes.
The precise outcome will depend on all the facts involved in the case, and the jury's decision based on those facts. So there is no single answer that always applies to every situation, but it sounds like you're wondering about some hypothetical situation that appears to be paradoxical because in this case only one person was charged with crimes: if someone else was the first shooter, the sequence of following events would first of all depend on whether or not they got charged with a crime, and I wouldn't characterize the outcome as a "win" or "lose" but as an "acquittal" or "conviction", and yes it is possible to be acquitted if everything is "accidental" as you described, and presumably not "reckless" (often meaning that a reasonable person in the same situation would have done the same thing).
About your more broad question: "Is mutual self defense a thing?" It depends on what crime is being charged against the defendant. In the Rittenhouse case there was only one person that was charged. If you're asking about a hypothetical situation in which two people involved in a 1-on-1 conflict both claim self-defense, I hope I can assume that they were both charged with a crime against which to defend themselves in court in the first place. It is indeed possible for a State to prosecute both parties of a 1-on-1 physical conflict, and for both of them to successfully claim self-defense in order to eventually be both acquitted. It wouldn't be called "mutual self-defense", but each defendant would make their own self-defense case individually.