Mmmyyyeeeeh. Wikipedia page for Pie says otherwise from what I can see? It needs to have some sort of filling, and the crust needs to be a type of casing, whether a cover/top casing or bottom casing, or both. The only mention of pizza that I can see is a link to the page for Chicago style pizza like here, as well as calzone, which both seem to fit the definition of a pie as described.
I’ll stretch to concede that this style of pizza is both a bastardized pizza and a pie, by modern/conventional standard. But not all pizzas are pies. Good compromise.