While the suffix '-ism' does generally denote a belief system*, the suffix in this case is attached to the 'theism' part of the word. The 'a-' prefix negates the rest of the word. Thus 'not theism'.
*Although...
*Although...
At the age of five, Skagra decided emphatically that God did not exist. This revelation tends to make most people in the universe who have it react in one of two ways - with relief or with despair. Only Skagra responded to it by thinking, 'Wait a second. That means there's a situation vacant.'