According to one definition among several possible definitions. Which definition is more useful will depend on the question you're asking.

For example, agnostics are not theists, therefore they are a-theists - according to one possible definition of the term. Similarly, ignostics do not take a position on the existence of gods, therefore they are agnostics - according to one possible defintion of the term. In both case, you could argue that agnostics are not atheists, or that ignostics are different from agnostics. That does not mean that the binary classification theists/atheists or the tripartite classification theists/agnostic/atheist is wrong - it just means that you're asking a more nuanced question that requires a more nuanced terminology.