Kind of a weird video. It basically comes down to "This isn't Neopolitan Pizza so it's not as good."
Neopolitan pizza has a whole association that certifies restaurants and Lombardi's isn't on that list. It's no surprise that the pizza will a different style.
It's also pretty funny he mentions that in Italy they fold their pizza, when that is practically the defining characteristic of New York style pizza.
Neapolitan pizza is one thing, Roman pizza is another, and much more akin to New York-style pizza. One type is made in big rectangular pans and sold by weight, it's similar to Focaccia. There is also a round style that is thinner and crispier, which is the best IMO. Fold and eat.
While I do enjoy a good old-fashioned Neapolitan pizza, I much prefer the Roman style, specifically the round thin style and by extension the NY style.
Dominoes is not American pizza as much as McDonald's are not American burgers.
Go to an actual good pizzeria in New York and if you still complain about it, im going to assume you are lying.