Well, first of all, it's called that in the actual game (protip: pressing pause, you can see the name of the room you're in at the top of the menu!)
Also:
—Right then, we’d like to ask you some questions about that improved story. First, was Kairi coming to Destiny Islands fate or was it just coincidence?
NOMURA: It was both. It’s not shown in this game, and it’s a delicate issue whether I can call this a living setting, but anyway Kairi was sent out from Hollow Bastion by Ansem’s hand. And the reason why Ansem sent her was to find the Keyblade. There was actually evidence of that in
the jail at the End of the World. Ansem thought that girls who are princesses would be sure to make it to the place of the Keyblade. So Kairi coming to the place with Sora and Riku was both chance, and also fate.
—When you look at the computer in the “World’s Prison” there is a message with a very deep meaning. It says, “Two will seal the Door of Darkness”. Who specifically is it referring to?
NOMURA: Well, judging by what happens (in the game), one of them is obviously Sora. As for the other one, you could take it as either; there’s both Riku and the King. And for the “two keys” after that, there are both the keys that Sora and the King have, but also there’s the presence of Sora and Riku.
—Well then, when Riku has returned to his own body, why doesn’t he come back to the world on this side?
NOMURA: That’s another thing I’ve been asked by lots of people, but the answer is actually written in
the World’s Prison computer message. It is implied there that only darkness can pass through that door. Riku and the King are not creatures of darkness, so they can’t come out through that door.
