The law that New York passed does not create any cause of action, it overrides existing rules regarding time-barring of civil claims, so the quick answer to the question "does this law apply in that kind of case" is "that law is irrelevant". There is a general legal question about the jurisdictional limits of a court. For example, a foreign insurance company will be subject to specific personal jurisdiction in a US federal court over a claim under a cargo insurance policy for a shipment to the US.
Daimler AG v. Bauman seems to be similar to the type of case you are asking about. This case involves the Dirty War of Argentina, and the question of whether Daimler's business connection to Mercedes-Benz Argentina gives plaintiffs standing to sue in US courts over actions in Argentina. SCOTUS held in that case that
Daimler is not amenable to suit in California for injuries allegedly
caused by conduct of MB Argentina that took place entirely outside the
The court first notes that
For a time, this Court held that a tribunal’s jurisdiction over
persons was necessarily limited by the geographic bounds of the forum
but this has been modified to
recognition of two personal jurisdiction categories: One category,
today called “specific jurisdiction”...[which] encompasses cases in
which the suit 'arise[s] out of or relate[s] to the defendant’s
contacts with the forum' [and] distinguished exercises of specific,
case-based jurisdiction from a category today known as 'general
jurisdiction,' exercisable when a foreign corporation’s 'continuous
corporate operations within a state [are] so substantial and of such a
nature as to justify suit against it on causes of action arising from
dealings entirely distinct from those activities.'
The court observes that "general jurisdiction has not been stretched beyond limits traditionally recognized". As I understand the hypothetical, the proposed wrong does not derive because of the defendant's connection with the jurisdiction, and the connection to New York (or any other state) would be that it might be forum convenient for the plaintiff to litigate in.
This would fall under the category of "general jurisdiction" (assuming that New York is not the company's corporate home nor is it their primary place of business), and the state's courts would not normally have jurisdiction in that case (lacking any specific statute creating a cause of action and explicitly declaring extraterritorial jurisdiction). The underlying constitutional rationale is the Due Process consideration that a person (including a corporation)
should not be be forced to defend themselves in courts in states where they have no real connection. The question that would be asked is whether the corporation had sufficient connection to the state that the state courts would have jurisdiction.
We should also turn to three SCOTUS cases, Nestle v. Doe et al, RJR Nabisco, Inc. v. European Community and Kiobel v. Royal Dutch Petroleum Co., where questions of extraterritorial jurisdiction are considered. The Nestle court's analysis of the underlying principle starts by observing and citing from RJR Nabisco that
First, we presume that a statute applies only domestically, and we ask
"whether the statute gives a clear, affirmative indication" that
rebuts this presumption.
In Kiobel, the court states – reaching further back to Sosa v. Alvarez-Machain that
[w]hen a statute gives no clear indication of an extraterritorial
application, it has none,
a principle which "serves to protect against unintended clashes between our laws and those of other nations which could result in international discord) (EEOC v. Arabian American Oil Co).
The relevant statute under which these suits were initiated is the Alien Tort Stature, 28 USC 1350, which allows an alien to sue in US courts under certain circumstances, and states only that "The district courts shall have original jurisdiction of any civil action by an alien for a tort only, committed in violation of the law of nations or a treaty of the United States". ATS would clearly not be applicable to the case of a US person suing a foreign corporation, but the other cases have articulated a principle that transcends the specifics of the ATS – there would have to be a statute giving a state extraterritorial jurisdiction over the matter.