Tried our hand at making deep dish pizza for new years. Turned out quite good but I'm no expert so I can't say how accurate it was. I am told the toppings are supposed to all go under the sauce but I couldn't resist putting some pepperoni on top
No judgement but here in the UK this is more like what we'd call a flan than a pizza or a pie. So instead of arguing about pizzas and pies, why not embrace a third category?
I would say a quiche /ˈkiːʃ/ requires eggs whereas a tart doesn't (necessarily), and I have no idea what a key-tch-zah is, we don't have them in the UK. A quiche is a type of tart though, yes.
Going by primary ingredient I guess it would be like a tomato tart. Though the dough is yeasted so it probably doesn't fully match a lot of categories.