Hi!
Well, it depends on how present the fairy tale aspects are. If the park is fairy tale-themed, but the fact it is fairy tale-themed doesn't contribute to the story (i.e. the story would not change very much if it had another theme), I'd say it wouldn't be fairy tale enough. If the attractions/rides are a significant part of the story, then it absolutely fits (and the looking-glass type scenario would absolutely fit, as it would be a reference to Alice Through the Looking Glass).
Good luck with the game!