Today the world "Palestinian" refers to only Arab Palestinians. Before the founding of Israel a Palestinian was a any person who lived in Palestine. It is the first sense of the word that I use here.
Gaza and the West bank are Palestinian because these territories were like Israel once part of the Ottoman Empire and then the British mandate of Palestine. The Ottoman Empire was divided into such mandates and to some extent countries. Turkey was created for the Turks, Saudi Arabia was taken by a revolution, other countries were created as Arab countries, ruled by the Hashemite family (Jordan and Iraq). Palestine was itself divided into a Jewish part and an Arab part. Gaza and the West Bank were essentially that Arab part.
Some other Arab countries, and mercenaries from Jordan and Iraq (the Hashemites have traditionally few problems with Jews) then invaded Palestine and while Israel could defend itself, the Arab part fell. Israel was attacked several times after that and eventually occupied Gaza and Sinai (taken from Egypt) and the West Bank (taken from Jordan).
Sinai was given back to Egypt in exchange for peace (and the Egyptian president responsible for that treaty was murdered by the Arab fascists for it).
Gaza and the West Bank were kept by Israel.
There was no justification for Jordan and Egypt to occupy and annex (Egypt annexed Gaza, Jordan did not annex the West Bank, I think) Palestine (the Arab part of it, I refer to that part as Palestine from now on), as it was meant to be the homeland for Palestinian Arabs.
Now that Israel controls these territories there is finally a chance for such a country (Egypt didn't want Palestine to exist as an independent country, Jordan didn't want Palestinians to have more power).
Israel won the territories legitimately, when it was attacked. But the countries Israel won them from did not legitimately own them.
Gaza and the West Bank were supposed to be Palestine and can now be.
And Israel said as much in a treaty with the PLO (which the PLO broke many times).
And the Palestinians ought to have a state.
And since the Arab fascists didn't want the Palestinians to have a state, I think it is obvious that they should have a state.
And that's why Gaza and the West Bank should be Palestinian (i.e. Arab).