It was originally released for the PlayStation 3, Xbox 360, and PC. However, the game is not backward compatible on the PS4, so it cannot be played on that platform. No. The first Call of Duty that was released for the Xbox One and PlayStation 4 was Call of Duty: Ghosts, one year after Call of Duty: Black Ops II.
Black Ops 2 is a backwards compatible game, which means that you can play it on the Xbox One even though it was originally released for the Xbox 360. To play Black Ops 2 on Xbox One S, you will need to either have the physical disc or have purchased the game digitally from the Xbox Store.