Remember that IDE CD drives have a special audio bypass cable that sends audio directly from the drive to the sound card, bypassing IDE, the CPU, etc. When you play an audio CD in such a drive, the machine only has to send special commands to the drive such as "play audio track 3," etc.
I also have a drive with such a button and presume all it does is "inject" such a command as if the computer had sent one.
All old-school audio CD player software on a machine will work that way -- all they do is send a small command to the drive telling it what track to play, and it does that and sends the audio directly to the sound card. So there isn't any quality difference between different audio CD players.
Now, all this is in contrast to "ripping" a CD--where the drive goes into a different mode where it actually reads the audio data and sends it back to the CPU over IDE. It's no different than what people had to do to upload a CD to a filesharing site, except instead of converting the audio data to MP3 and writing it to disk, it sends it out the sound card and throws it away. I believe WinXP and later had an option for "digital" audio playback where it plays all audio CDs this way. And MP3 playback has to work that way.
For software I would poke around http://www.ibiblio.org/pub/micro/pc-stuff/fre … les/util/sound/ as it looks like mpxplay might be what you're looking for