Beginner's Guide to Atheism.

[Athene]

Huggy's right in that 'ism' denotes a system.  That system is theism.  The prefix 'a' is negation.  So, 'atheism' literally means 'not-theism' just like 'amoral' means 'not-moral' in the sense of being not connected to/involved with those things rather than in a pejorative sense (which would be 'antitheism' and 'immoral' respectively).

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?

Mmmm....NO. I think Kevin is correct on that particular point.

You are kind of on right track though, IMO....at least to some degree. The most publicly visible brand of capital "A" Atheism, though not a religion by definition, exhibits so many of the negative trappings of religion that it's virtually indistinguishable from it in regards to functionality, save for the lack of belief in gods. 
The fundamentalism, indoctrination, fanaticism, idolatry, and the sanctioned "preaching" of intolerance, imperialism, misogyny, and racism being "righteously" defended as a means of "following the logic" to the end sure as hell seems to take on the flavor of religion, in my view. Big time.

That's one of the reasons why I (and I imagine many others) have no interest in being aligned with the "Atheist Movements" at large.

Atheist religions exist, this is fact. 

New Atheism fits the bill, in my book.


So, I'll allow it.

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

I think the aforementioned would best be filed under "Deez".