Cyrem had me test a utility that will force an unmodded game to play music files from a folder. It worked, so he uploaded a guide. Try this:
As for why the CD plays audio when inserted into a CD player... this was extremely common in the '90s, and I think it first started because early CPUs may not have had enough power to both process CD-quality audio and do other things at the same time. Some CD drives from the era had a small cable that plugged directly into the sound card, which meant you could bypass the CPU entirely. The CD drive would treat the disc as an audio disc (Redbook format, usually) when necessary, which meant the audio had to be on separate tracks that were compatible with other music players. I actually remember this being an issue with one of my computers around 1995. Regular sound effects would work in some games, but the music didn't play. Later my dad fixed it by plugging a second set of speakers into the headphone jack of the CD player. We had to have both sets of speakers on to hear both music and sound effects. I still have a computer with this sort of cable connected to the CD drive.