It's probably because Sound Blaster Pro has switched channels by default and since Audician card pretends it's a Sound Blaster Pro, Quake switches the channels automatically to the "correct" configuration. It's just guessing but entirely possible. I'm sure there is something you can do about it, Quake was the most customizable game of it's time.

It's a whole thing and not as simple as it might be: Re: SBPro1 CT1330A owners, care to help figuring things out?

Quake doesn't do this on a real SB Pro as you can see above. I've looked into all of the options Quake allows for config, both in game and command line, there's nothing for reverse stereo. At this stage it looks like my options are to physically reverse the plugs on my audio cable (bleh) for this one game or hack the mainframe and try and fix it. The source for QDos is available I notice so I guess I could have a poke around in there (bleh).

Good old winquake works fine so that's an option.

Is there an option to reverse channels in Yamaha mixer utility? I cannot test it myself now. It's a weird issue that will probably have a solution, I mean other than turning headphones 180° or similar. I am surprised there is no setting in Quake that addresses it.

There's no channel swap feature in YMF71x chips.

I don't recall having channels swapped in Quake but it has been a long time since I played it (not among my fav games 🤣)...

I seem to remember reading somewhere that the YMF718 has reverse stereo for PCM but correct for the wave table header. The opposite for the YMF719, correct stereo for PCM but reverse for wave table. Haven't tested that myself.

The reverse stereo on WB header is a board error on the common Labway card. Other cards I have come across with don't suffer from it.