I know we are just splitting hairs here, but the GH is
LIKE God.
A god would be omniscience, omnipotence, omnipresence, of which the GH (you and me) do not possess in the game. Doest that make sense? Again I think this is just splitting hairs, but it still needs to be pointed out.
Gods (with a small "G") need not be omni-everything. Look at the Greek, Roman, Norse, and other ancient gods. They were felt to be like super-powerful human beings with human failings and weaknesses.
Now, if we were referring to God with a capital letter, that would be a different story ...