No, I have not committed the fallacy of false dilemma. I have not fallaciously concluded the existence of any God that you have named.
Then I apologize for making incorrect assumptions about your beliefs. Let me explain my position.
Assertions about atheism made by non-atheists are commonly overstated, in my opinion. I live in a largely secular country, and have both lived and spent considerable time in other largely secular countries, or working with a lot of people from those countries (in particular New Zealand, also Sweden).
There is a lot more variance among atheists than you would believe if your exposure was limited to the internet, or to majority-theist locations. (Note: 'You' doesn't mean you personally...I'll try and make no further assumptions from that end, at least in this thread!)
Sure, we can call them agnostic (and I refer to myself as an agnostic atheist). I thought long and hard about how to label myself. Not so much because the label matters much, but that's just how I'm wired.
But these people don't believe in Gods, and are not theists. Unlike what I would think of as a 'pure' agnostic, they are not saying the whole question is indeterminable in a philosophical sense, although some (again, like myself) would say it's indeterminable in a scientific sense. Rather, on the balance of evidence...or lack thereof...they are saying that they don't believe in Gods...or even gods.
Again in a philosophical sense, not all Gods/gods can exist. Or, rather, if they do, they do not exist in the sense that people believe in them.
A simple contrast of monotheistic beliefs illustrates this. More than one god claims to be the one god, which means either;
Not all gods we believe in are real or
Not all gods we believe in are as we believe them to be.
So, can I prove Tiddalik doesn't exist? No. I'd go further and suggest such a thing isn't even possible.
If you wish, you can think of me as an agnostic for that reason. I do.
But I add 'atheist' to my label because I find it disingenuous to describe myself only as an agnostic. I think, on balance, it is very unlikely Tiddalik exists. I see no reason to believe Tiddalik exists. Calling myself an atheist gives a much better approximation of my lack of belief, although it says very little about what philosophies or world views I hold.
Sure, it bothers me even more when atheists pretend atheism is more than it is than when theists do it. But that' the thing about atheism...there is no entry requirements. They're just as atheist as me, even if I think their understanding of atheism is flawed and confused.
To whit...there is no 'thesis of atheism', but instead a whole raft of conflicting beliefs around it, most of which are horribly overstated. That is why most atheists would state that there is no thesis. What they really mean is that there is no commonly agreed thesis, and atheism doesn't require it. If you would then suggest that this means atheism doesn't hold any real value at all, then I'd completely agree. It doesn't.
As for distinguishing it from agnosticism...well, sure. That's one way of labeling the world. I prefer to combine the two labels, much as one might say they're an Italian-Australian or something. Does it provide definitive information on my beliefs? No...but is it slightly more informative than calling myself 'atheist' or 'agnostic'? I think clearly yes.