This is an incorrect linguistic analysis. The prefix "a-" in English usually only attaches to adjectives, as in
a-political,
a-moral,
a-symptomatic, etc. We do not have corresponding nouns
*apolitician, *amorality, *asymptom. There are a number of nouns with that prefix that were borrowed into the language with the prefix already attached, as was
atheism, which was borrowed into English from French. That happened in the Middle English period when a great many loan words came in from Norman and Parisian French dialects. French and Latin were the language of the clergy at the time.
More importantly, though, we should be careful not to fall into the trap of an
etymological fallacy, where meaning is based wholly on historical or morphological analysis. Usually, lexicographers derive definitions from a corpus of example usage. This survey is intended just to gather intuitions about how people in this debate forum think of the word "atheist" and "theist".
This is a good thing to point out. In our community, we get into debates with people who have all sorts of beliefs. Hence, we have a need to distinguish a lot of different flavors of theism and atheism. That affects how we use the word "atheist", which now takes on a more generic flavor than it might have outside of this context. We are very much like a technical community that has developed specialized word usage and vocabulary to meet its need for greater precision in communication.