There are two ways of playing CD audio: digital (in fact grabbing, this does not need the cable from CD to soundcard) and analog (older one, needs cable connected to the soundcard).
Windows Media Player knows both and it defaults to digital (there is checkbox "Digital" somewhere in menu). If the game has CD Audio you probably need the cable (the game does not do grabbing, it just tells the CD to play track XY and the sound from CD mechanic goes to soundcard).
If you have the analog connection from CD to sound card then it is ok (some CDs/soundcards enable digital connection as well, I do not have experience). But there must be some connection (otherwise only grabbing is possible).
Mirek