Can confirm I'm having all the same issues as OP on Proton 7.0-1, on Steam Deck; no videos, no ingame music.
The FMVs can be fixed by using the DLLs from either cnc_ddraw or dgVoodoo2.
https://bugs.winehq.org/show_bug.cgi?id=2082
The music can be fixed by setting winmm to n,b. This is because Outlaws+AHoM ships with a WinMM replacement that emulates the CD music.
Compatibility Report
System Information
I confirm:
Symptoms
Several problems. No video in movies (though you can hear them). No music in game. When you try to change the mouse config, some people get a crash, but I get a distorted, blank grey (win98 style) box with no options that can be selected. I cannot alt+tab out of this and must hard reset computer. Some others said they couldnt change resolution but since this is an old game I wasnt aware you could change resolution, so thats not tested
steam-559620.log
Reproduction
Start game, try playing game. Try changing mouse config.