Beginner's Guide to Atheism.

[Amarok]

No dummy, 'atheism' (a = without, theos = god, ism = system) literally means a 'system without god'. A theist can believe a god exists without being religious, but theism is a system based around a belief in god also known as religion. If an atheist is one who simply holds no beliefs in a god, then atheism is a system based on the non-belief of gods... Got it?

Nope the ism suffix is not a system it's a state . Without a belief in god (a = without, theos = god, ism = state of mind or an attribute  )  . The ism does not denote ideology it denotes a personal state of belief . Being no belief . So this statement is bullshit 

Atheist religions exist, this is fact. 

Even if that were true . Atheism itself is not a religion 

That being the case, under which category would an atheist religion be filed, theism or atheism?

Neither because atheism is not a religion