jnisbet: The reason why changing the name of olwin.exe to something else fixes the music is that the GOG installer adds compatibility settings to the registry which apply to olwin.exe, but not to executables with different names.
The offending registry settings are in the following locations:
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Custom\olwin.exe
Delete that key (folder).
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers
In that key (folder), find the value that points to olwin.exe, double-click it and remove "DISABLETHEMES" from the list.
Of course, it's an easier solution to simply rename olwin.exe, but this is what you can do if you're comfortable with editing the registry.
Edit: Here's a registry file that I've made to do the edits for you. Paste the lines into a text file, name it something.reg and double-click it.
https://pastebin.com/sFKfrsNE Thank you so much! That gave me Outlaws music back. With Outlaws, music is 50% of the experience!