I think I understand that definition. An atheist is someone whose belief system does not include any belief in anything they call “God” or “god.” By that definition atheism is not a position that needs to be defended. Actually now that I think of it, I disagree that it doesn’t need to be defended, but I’ll come back to that. Letting that stand for now, that atheism is not a position that needs to be defended, when people are maligning and scolding people for their belief in Gods, that is not atheism, that is anti-theism, and carries as much burden of proof as any theist position.
I realized as I was writing that, that even defined as lack of belief, identifying as an atheist can be position that carries a burden of proof as much as any other. Sometimes means that a person has decided that anyone who has any belief in any god or gods is wrong, and that is in fact the position that atheists are arguing from most of the time in online debates. Again, if I wanted to challenge what atheists say in online debates, I would not be challenging their lack of belief. I would be challenging the belief of some of them that any belief in any god is always wrong.
I'm an atheist and have been all of my life. I do not claim that there cannot possibly be a god, but I can say that none of the gods so far proposed seem to have any good evidence to support belief. So for me, it is simply a lack of belief in a proposition, or more accurately, a host of propositions, and that does not carry a burden of proof (although I can give reasons for not believing). There are certainly atheists who do declare that there is no god of any kind in the universe. I only disagree with them because I cannot prove the absence of any sort of god at all with absoluteness. However, I feel the existence of a god is about as likely as the existence of unicorns, or fairies, or any number of other such things. This avoids many endless, fruitless discussions with theists who will insist on absolute proof from me, while proclaiming the existence of their god without providing equivalent absolute evidence.
Yes, an atheist would believe anyone that believes in any of the thus-far proposed gods was incorrect. But he can do so without believing that there can be no sort of god at all.
Part of the problem with conversations like this is the theist will simply use the word "god" without providing any description of the god, or it's attributes, or what it does or does not do. So an atheist will have no idea of what god is being discussed. Even if one knows one is conversing with, say, a Christian, one cannot be certain of the nature of the god in question. It seems sometimes that there are as many versions of the Christian god as there are Christians. It is positively mind-boggling. An then at the end of the day, when one asks for a clarification to understand what sort of god is under consideration, the response is "god is unknowable". That is a show-stopper. But is is a dodge to avoid having to clearly define the god.
Well, I'm drifting off the mark, so I'll end here........
I very much agree with your comments about anti-theism, though.