That isn't pizza but a delicious pie that is pizza flavored. Pizza generally will have a thin crust or is typically eaten with the hands exclusively. Pie on the other hand will be eaten with a fork (and maybe knife) like what is served in Chicago as "pizza"

As far as "Dish" I really don't care enough about that it is pretty common terminology at this point and it is as far as I know not tied into a company like making a Xerox or wipe my nose with a Kleenex or something. Sheldon Brown lists it in his glossary of terms as does Park Tool and Wheel Fanatyk. Yes it is technically centering but I think at this point dish is used enough by the industry and industry professionals that we can accept it.