Well, who am I to argue. It's been a long time since I played the game and interpretations may vary, I can't really remember that much from the game itself, so some of my arguments may be flawed that way. I may come back with a rebuttal once I read into the script more

And no, the idea of theocracy is that there is a god in the center of the religion (theos was Greek for god). Ancient Egyptians had a theocracy because they believed the Pharaoh was a god incarnate, therefore, his will must be fulfilled without protest. So while this often does overlap, just having a religious institution run a country does not constitute a theocracy, like in this example, where there is no central deity.