The style they are doing is Neapolitan style pizza, the hallmark of which is crust that can be folded without cracking AND which is supposed to be eaten with a fork and knife. It is 100% authentic in that respect.
OP, the pizza is fantastic. Fresh, high quality ingredients, and minimal ingredients at that. Nothing fake. The cheese is fresh mozzarella so it is a different taste/texture than processed mozzarella. That type of cheese gives off water when it melts which contributes to the soggy factor, which is also why they don't put a lot of cheese on the pizza.
The pepperoni pizza there is the best I've ever had. I visit their CA restaurant here in Downtown Disney Anaheim (Naples/Napolini) at least once a month. They sell the pizza by the slice here and it is consistently the best Neapolitan pizza I've ever had. I grew up in NJ and this pizza is another level good.
I have found that people who don't like it are simply not aware of what Neapolitan pizza should be. If you go to Southern Italy, this is what pizza is like there.