The atheist position, if stated correctly, is a belief there is no god based on the fact there is no evidence of god. This is different than simply being non-religious or impious (not a worshiper of any god).
God is not an atheist. He has evidence of his own existence and therefore cannot believe he does not exist. However, god is also not theist. Theist hold that god has a particular form. God himself claims he has no form at all except a mask he uses to fool the theists.
God is in all likelihood an apatheist. He just doesn't consider the question of his own existence to be of any importance to himself.
On a side note: There are many instances in Hindu religion where you see gods worshiping other gods. So it doesn't appear that the Hindu gods are atheists either, but for different reasons.
Interesting fact: The word "atheist" existed long before the word "theist." Originally, an atheist was a person who denied the existence of one particular god, usually the state-god, but not necessarily all gods.
Theist is a term that was invented to distinguish pagans (later polytheists) from people with one god (a new concept in antiquity). A theist holds that god typically has one form and personality by which he (always he) can be identified. Believing in god does not make one a theist. Believing in a god of one form makes you a theist.
If you believe in a god of all forms, you are a pantheist.