Okay, so I know a few more things now: one, this is clearly the first installment of the series; Kairi has short hair, no one's mentioned King Mickey, and Riku doesn't seem nearly as tense as he was after the whole "Ansem" fiasco. There's a chance that this could all be taking place inside Castle Oblivion, but I tend to doubt that.
For one thing, Castle Oblivion has a much different layout than any of the locations in the first game; that's the PS2 version, of course. I'm not about to go out and blow who knows how many bucks on a Gameboy Advance just to play one measly game. Another big thing that makes me sure I'm on the real Destiny Islands - God help me, I can't believe I just wrote that - rather than the ones that Castle Oblivion created is the presence of Kairi, and a Riku that's not dressed up in "Ansem's" infamously hilarious hula dancer from hell getup.
Still, what I'm actually going to be able to do about anything remains to be seen.