Greek culture was and still is an Eastern Mediterranean civilization that has deep roots in Anatolia and that had and still has way more in common with other Eastern Mediterranean cultures than Western European cultures. There is no hard European/Asian line, only a smooth Eurasian continuum.

That Westerners and Hollywood try to pitch Greekness as some kind of Western outpost in the East says way more about their own Orientalism and, frankly, racism, than it does about Greek culture which, you know, just exists, regardless of what Hollywood has to say.