I'm not too sure that atheism can be translated as non-theism. I seem to recall an article (or something, that I have neither a title nor a link nor any other form of reference for) that agreed with Nyarly's definition for atheism, 'lack of belief in the existence of any form of supernatural power, entity, etc.' I think the problem here is just a confusion of the words, as they are (ridiculously) easy to transpose (atheism and nontheism). Nontheism is, I think, better defined as 'lack of concern regarding the existence--or nonexistence--of any form of supernatural power, entity, etc.' To put it simpler using a part of a discussion I once had with a friend on this topic:
Ask four people if there is/are (God, gods, ghosts, any other supernatural force).
A theist will say 'yes'.
An atheist will say 'no'.
An agnostic will say 'I don't know'.
A nontheist will say 'I don't care'.
(I know this is simplifying an impossibly complex issue to an almost ludicrous level, but it's only for illustrative purposes to hopefully help people form their arguments in more productive manners. If it helps someone, great; if not, just think to yourself 'well, this guy's an idiot' and move on with your discussions. Thank you.)