—But an antitheist could not be an agnostic. Therefore it makes sense not to put both beliefs under the same term.—
I don’t know what you mean. Under what same term? They are both descriptions of different things.
My car is blue. It can also be large OR small (but not both). However, it’s size doesn’t change it’s color.
—Imagine a world where nobody can be absolutely sure of anything.—
Ah: ok. So we’re talking about the real world then? 
—Nobody could believe in god without any doubts.—
This would have to be a characteristic of the people in the world: not the external world itself. No matter how uncertain the outside world becomes, absolute belief cannot be precluded unless it is precluded by the psychological makeup of the people. But I still think you’re confused, because you keep emphasizing this concept of “absolute,” which is totally foriegn to the terminology I’ve used. I am not classifying anything by it’s “aboslute” tendancies, i.e. absolute proof, absolute belief. The distinction is: believe or not.
Questions of absolutes, or at least degrees of certainty, are questions specific to epsitemologies: none of which terms like “theism” or “atheism” can presume (especially since a given person may not even HAVE an epistemology). One’s own reasons FOR belief, personal cases and subjective burdens of proof, which differ wildly from person to person, are not relevant to this level of definition: and thus neither is “absoluteness.”
—Therefore everyone in the world is an athiest according to you.—
If there were a world in which no one had heard of the concept of god, we would have a world full of atheists. Likewise, if all theists suddenly disappeared (perhaps taken up in an expanded rapture?). Likewise if all people above a few months old died.
—Does this mean there is no reason for debate in this world?—
No: there is plenty of reason for debate on just about anything. Even if there are definately no theists, atheists can still argue the theist position in the name of learning.
But as soon as someone ends the debate in their mind, and starts believing that god exists, a theist is born. For theists, taking this step is generally considered a GOOD thing, which is one reason why many theologians now concede that atheism is a lack of belief.
—Do people who believe in the nonexistence of god have no argument with those who believe that god almost certainly exists, but may actually be just an extremely powerful physical being?—
Yes they have very legitimate arguement with each other. I’m not exactly sure what you mean with the latter group though, because they are pretty clearly theists: thus destroying your own example.
—I just don’t see your terms as beneficial to debate. I see them as excluding people from the side they would naturally be on.—
I don’t understand: that’s nonsense. You can only meaningfully call it “excluding” if you AREN’T using my definitions anyway (how else could you conclude about which “side” they would “naturally” be on), in which case, what’s your problem?
People who believe in gods, for whatever reason, are theists. People who don’t, for whatever reason, are atheists. If nothing else, my definitions at least TAKE PEOPLE AT THEIR WORD as to what they believe, without trying to cut apart their reasons a priori. So where’s the “unnaturalness” of it all?
— It seems arbitrary to me that you insist that absolute certainty be a requirement for a god claim.—
How can we possibly have a productive discussion if you say things about me which are not true? I never said anything about any requirement of absolute certainty. I said: belief. There is a god claim. Will you affirm the claim as true? Or not? Your reasons are your own (and can’t possibly be factored into terms like “atheist” and “theist” because they are far far far too diverse among different theists)
—Actually, I do not think unfaltering belief should be required to make a god claim.—
Again: when did I say anything about unfaltering belief? All I said was that the characterization of theist rests upon whether or not someone says they believe in god or not. How could you possibly argue otherwise? I would have thought that, at least, the definition of theist would be uncontroversial, but now you seem to be advocating that something other than a person’s own admission of belief be the determinant!
—What if god exists such that it is impossible to have absolute belief in him? Your terms arbitrarily deny such possibilities.—
Nonsense. I haven’t made any sort of insitence on “absolute” belief. I said: you have a belief or not. Just like you have an apple or not. Either you are willing to affirm the truth of god’s existence, or you are not. Why you do, and what your threshold is for whatever epistemology might underlie your thinking (and there might NOT be one!!!) is your own bussiness, and doesn’t enter into atheism anymore than it enters into theism.