I made a (poorly titled) topic about this here: https://www.gog.com/forum/earthworm_jim_series/no_gold_edition
I just found my copy of the game in one of our filing cabinets so I yanked it out and gave it a whirl under Windows 10 x64.
The Sound FX are indeed broken, the first sound effect heard gets stuck in a 1 second looping loop that never stops until you turn off sound effects and the game seems to only be able to play 1 sound effect at a time so you basically just hear the start of the first sound effect ever played looping. You will need to apply Windows 98/ME or Windows 95 Compatibility to be able to turn on Sound FX, otherwise the option will be permanently disabled.
The music plays without issue.
You need to use Windows XP Service Pack 3 or older when setting up program compatibility or else it will crash trying to play some Electronic Arts video clip, alternatively you can avoid this step if you don't play the game via the Auto-Run program. Also the game features an EXE file named Killworm.EXE and virtually every Virus Scanner software's Heuristics functionality will freak out about it for no good reason.
Aside from sound effects being broken, the game seems to work pretty great? Don't know which levels are missing when compared to EWJ 1 & 2. The disc contains a Desktop Theme based on game assets. GOG could easily include the game with a warning that Sound FX are unlikely to work.