"a violent act or acts dangerous to human life that are in violation of the criminal laws of this state and are intended to:
(i) intimidate or coerce a civilian population;
(ii) influence the policy of a unit of government by intimidation or coercion; or
(iii) affect the conduct of a unit of government by murder, assassination or kidnapping."
You can, if you want, read his manifesto here. It's very much not trying to influence government. If he pointed out some specific government policy, ideally one up for a vote or something, then maybe there'd be a case. But as far as I know he didn't even do that. His whole deal is apparently "government failed, guess I gotta do something myself."
(Don't bother arguing about whether this was likely to help anything; our opinions don't matter. The statute up there is talking about his intent.)
And the civilian population of New York was kind of the opposite of intimidated! There were rallies for the guy, while he was at large. Presumably you think pretty badly of those people, but my point is that the population definitely was not terrified they'd be next.
So. Literally, by the book--like, the relevant book, the one they throw at him--Mangione is not a terrorist. I don't think there's even much of a case for it, and I strongly suspect that Alvin Bragg doesn't either. If they want to make an example of him, they will have to do it by prosecuting him for something he actually did.