Chacranajxy: Yeah, it's a lot more interactive than most visual novels. It's more along the lines of Phoenix Wright or 999, so maybe it's more reasonable to just call it a straight-up adventure game.
Well, visual novels come in many variations - RPGs, dating sims, adventure games...calling it "a straight-up adventure game" sounds vague at best and misleading at worst.
By the way, have you seen the anime? I ask because you call the story "amazing", and the anime adaptation's only sort of "amazing" was amazingly bad. It was really obvious that it's a visual novel adaptation (even more than usual), but I suppose it's possible that it was a bad one. On the other hand, the central contrivance is - I assume - the same, and that was...well, let's keep this polite.