According to leaker BKTOOR5, Gun Game is coming to Modern Warfare 2.
The leaker revealed alleged data mined files that showcased the presence of Gun Game and Gunfight in Modern Warfare 2. Unlike Gunfight, the devs never confirmed if Gun Game would make its way to the game, so take this leaked information with a grain of salt.
However, it is possible to play Gun Game in Modern Warfare 2 Private Matches, which bodes well for its chance of being playable in online multiplayer. As it stands, the arrival of Gun Game seems more like a matter of when than if.