But it's usually labeled with the regional descriptor intact, e.g., New York Style Pizza or Chicago Style Pizza. I think OP was just referring to the fact that pizza's region is Italian by default, and they are taking exception to the article omitting "New York Style", even though it was heavily implied, and apparent to all but a pedant.
There are quite a lot of foods and beverages which have a protected name bound to the ingredients that are allowed to be used to create it in a specific way. Take Mozzarella in general or for a local example beer in Germany(Reinheitsgebot).
It is not far fetched that Italian Pizza could be a candidate for a TSG marking. There are individual pizzas which already are protected, take Pizza Napoletana for example.