You are absolutely correct. Not only do none of the parties have any nexus to NY but none of acts which presumedly make up the lawsuit occured there either. Very serious jurisdictional issues here. I don't even see how a Federal Court would have jurisdiction.
This case has all the legitimacy of that useless post-9/11 civil suit against Osama bin Laden or the Iraqi government, in which a ridiculous trial was carried out and a "default judgement" of 100 million-billion-trillion-gazillion dollars was awarded to the plaintiffs.
I saw on TV that they apparently served the son on the plane when it arrived in New York, but before he deplaned. (It didn't say anything about the father.) That would raise some interesting questions if it was an international flight that had not yet cleared customs. I think there are a few cases out there that if you get personal service in the jurisdiction, you can sue them there, so they may be able to make a case as to the son, but they are certainly testing the limits of 'minimum contacts'.