(A) PC soundcards generally either have a single stereo analog Line Out (L + R) or if it has 5.1 analog it could have three stereo Line Out jacks - Front (L + R), Rear (L + R) and Center/Sub (or Center/LFE).
In either case they are all stereo jacks supplying a signal for two channels. If you only have two conductors (the yellow and white) and an outer braided shield, then the outer shield is likely the common ground between the channels and you may need it also patched back together to provide the return path for the two channels.
(B) If on the rare chance you have a soundcard with 6 separate line out jacks for each of the 6 channels (5.1), then it's possible that the braided shield would not be absolutely needed to have a signal and is used only as a grounded shield to prevent hum, but still is a good idea to have.
But my guess is that your soundcard has one of the (A) configurations.
Steve