Bruh, this dude have the campaign installed, but not the multiplayer nor zombies.
You need to download all 3 "Black Ops 2", they are listed in steam like if they were separated games. Or if you just open MP it should start downloading.
I just had the same error message and it was because of that, downloaded the game but for my suprise, its divided in 3 "games". Since I had only BO2 in favorite list, didnt saw the zombies and mp section. So just in case this works for anyone else