Something doesn't exist unless it actually exists. In this case, Okami, the outer world 2D or the 3D basing on 2D of another world or whatever you called it.
Something exists only when we know it exists, meaning that we need to back it up with proof. There is no proof for what you claim.
Something that may or may not exist, especially without any proof to back it up, essentially doesn't exist because in fact it doesn't. Sounds really silly but that's how it is.
Of course people believe in things that may or may not exist everyday like for example religion which you mentioned, but belief is a case by case thing so it's not really good to make such a generalization. And keep in mind that we human beings live by common sense and there is a line to how much you can surrender that common sense. In religion's case, the practice of believing in a god has mostly become part of common sense, thus it's justified no matter how stupid it actually is. Also, most beliefs (at least religious ones) have an intention or destination. Okami, I don't see any of that in your belief, nor does it follow common sense, nor does it have any proof. It's basically a random "theory" thrown in out of nowhere.