The reason the dash plays audio through is because it is PCM (2 channel), while the games are AC-3 (Dolby Digital 5.1 channel). You can switch off the Dolby Digital in the dash and just put it to stereo, and it will play PCM audio for both games and dash, but that won't take advantage of your new 7.1 channel system!
Your sound card should be able to decode the AC-3 signal coming through the optical and output it through the analog outputs on the sound card. The sound card must have a decoder built in, otherwise you wouldn't have Dolby Digital 5.1 sound when you play back a DVD on the computer.
What it means to decode is to convert it from digital to analog, like that decoder box you linked to does. You plug one digital cable in, six analog cables come out (one for each channel, or speaker) which connect to an external amp (the T7900 system).