yes, that's the ground of the sound card, and no it wouldn't cause this.
Have you looked at the pinout of the dual op amps? The pins are labeled - in, + in and out for both sides. Just connect them the same way as in the diagram.
Oh, and try this: disconnect the post amp and try to use the sound card as a sound card. play a 44.1kHz 16 bit stereo wav ripped from a high quality CD with high frequencies in it. Compare how the highs sound to how they sound from your reference CD player and the 'normal' windows sound card using some good headphones.