All humans are mammals. All mammals are not lizards. Therefore...?
Let us grant that all atheists are not theists. Neither are deists, rocks, polytheists, Buddhists, agnostics, etc. Saying that a property applies to all atheists no more characterizes all atheists than does the fact that all humans are mammals characterize humans. We are quite different from mice, bats, whales, etc., and there exists entire sets of finer classifications (such as our species and subspecies, homo sapiens and homo sapiens sapiens, respectively, or "primates") which testify to the importance of properties defining humans other than that they are mammals and the fundamental irrelevancy of a property universal to all instances/exemplars of a word/concept when that property is shared by so many other things.
In this case, your logic can be "paraphrased/rephrased" as follows: "All rocks are not theists. All rocks don't believe gods exist". Ergo...? (same with "all atheists are human", a property that, I would hope, you believe all atheists share but one which is true of all theists). Congratulations, you've found a property that atheists and rocks share. So what? Rocks aren't atheists.
Perhaps because this definition implies rocks are atheists, fails to distinguish between theism and other beliefs about gods, and isn't equivalent with the claim that atheists lack a belief about god or that atheists are those for whom a belief in god is absent ("doesn't believe god exists" can mean "believes god doesn't exist", as every person who believes god doesn't exists "doesn't believe god exists"). Rocks aren't atheists, and even if "all atheists are X" doesn't imply anything significant about atheists. A defining characteristic distinguishes the defined group/set/class/etc., from others in general, not from one other specifically.