Under the correct definition of "pie":
Whose definition?? An english language dictionary? The word pizza ain't english.
The Ancient Greeks covered their bread with oils, herbs and cheese. In Byzantine Greek the word was spelled πίτα or pita, meaning pie. The word has now spread to Turkish as pide, in Balkan languages: Serbo-Croatian pita, Albanian pite, Bulgarian pita, Modern Hebrew pittāh via the Judaeo-Spanish pita. Though the Hebrew word pittāh is spelled like the Aramaic pittā, which is related to Levantine Arabic fatteh, they are not connected historically.The Romans developed placenta, a sheet of flour topped with cheese and honey and flavored with bay leaves. Modern pizza originated in Italy as the Neapolitan pie with tomato. In 1889, cheese was added.