You might be able to pull it off by installing a fresh copy the Steam client to the target drive, moving the target game over, sign into your account, then select the game and use that "Verify Game Files" option (or words to that effect, I forget the exact option). This should replace any pieces that got lost in the transfer.
Now, if you're going from platform to platform (i.e. Windows > Linux)? No, you'll need to a complete fresh install of game.