Not much left of that doctrine anymore. See, e.g., Shaffer v. Heitner, 433 U.S. 186 (1977).
But it is still there, and it fits this case, provided it can pass all the constitutional hurdles.
Plus there’s the fact that they have a diplomatic presence in the US. Back in the day when I worked in a law office in NY, we once sued France for something or other, and served papers on their consulate. If a foreign power or entity with a New York diplomatic presence shoots people indiscriminately in Israel, and injures a New York resident, my gut tells me that this power or entity is subject to US jurisdiction in New York state and federal courts.
Finally, New York jurisdiction in Products Liability cases is based on even flimsier tenets. So long as the product is made by a company with ties to interstate commerce and hurts a New York resident, there you are. I submit to you that terrorist organizations have ties to international commerce, and in fact exist to disrupt it. They did so, by harming Americans who were visiting Jerusalem. Ergo, they are liable for the faulty guns they used that do not misfire when pointed at a human being, such as those used in West World.