What is a Mystery Game?
A mystery game is a game in which a mystery is the central element of the game.
That is, without the mystery, there wouldn't be a game.
Take the game of "Clue", for instance. In this classic board game, Mr. Boddy has been murdered, and it's up to you to find the killer. Without the element of mystery, there wouldn't be a game, there would just be players moving around a game board with no particular purpose. The mystery is the central element of the game.
Other games, while they may contain mysterious events, are not really mystery games. The mystery is mere decoration, and not an integral part of the game.
Admittedly, this definition of "mystery game" is a little fuzzy. Fact is, the term "mystery game" can accommodate a wide variety of settings and gameplay mechanics.
I think it comes down to this: If you take the "mystery" out of the "mystery game", is it still a game?