Is this a Definist and/or False dichotomy Fallacy?

I was looking at an academic post on the definition of Atheism by plato.stanford.edu site. Now, I am not suggesting that the source itself is defining Atheism in this way; it could just be the signifying how it is often defined by certain others. However, an excerpt from the post that I wonder about being fallacious is as follows:

1. Definitions of “Atheism”

“Atheism” is typically defined in terms of “theism”. Theism, in turn, is best understood as a proposition—something that is either true or false. It is often defined as “the belief that God exists”, but here “belief” means “something believed”. It refers to the propositional content of belief, not to the attitude or psychological state of believing. This is why it makes sense to say that theism is true or false and to argue for or against theism. If, however, “atheism” is defined in terms of theism and theism is the proposition that God exists and not the psychological condition of believing that there is a God, then it follows that atheism is not the absence of the psychological condition of believing that God exists (more on this below). The “a-” in “atheism” must be understood as negation instead of absence, as “not” instead of “without”. Therefore, in philosophy at least, atheism should be construed as the proposition that God does not exist (or, more broadly, the proposition that there are no gods).

This definition has the added virtue of making atheism a direct answer to one of the most important metaphysical questions in philosophy of religion, namely, “Is there a God?” There are only two possible direct answers to this question: “yes”, which is theism, and “no”, which is atheism.

plato.stanford.edu/entrie. . .

Yes, and I think this is why so many atheists objurgate the term atheist.

Because it is defined as an objection to theism when most atheists reject the first premise of theism. Why should they be defined as someone who rejects an impossible idea in the first place?

I often see people trying to argue what atheist means......to atheists. That would seem to be the definist fallacy, as they are likely doing this with the sole intention of shifting the burden of proof.

One of their go to arguments seems to be to link to a philosophy website which says that atheism is a belief that there is no god. The thing is, not accepting the claim of theism due to a lack of any supporting evidence doesn't lead to any questions or lines of argument/reasoning, so in philosophy it's functionally useless and thus pretty much requires it to be an opposing position. However, when someone identifies as an atheist they're not engaging in philosophy, they just don't believe in the claim, so pointing to a philosophy definition is irrelevant and is a form of equivocation.

It wouldn't be a false dichotomy as a god either does or doesn't exist, but theism/atheism only deals with one prong of the dichotomy, just like how a court only deals with guilt and doesn't address innocence at all.