I get this game to run on Wine, but I can't seem to change its resolution. Did anyone here manage to get it working?

If you use 3dFX Open GL, then the in-game resolution setting isn't relevant, and the way to change the resolution is by running nglide_config.exe from the Sin Gold installation folder.

The in-game menu will always display as 640x480, regardless of what your resolution is set to in the nGlide configuration program. But once you're in the game, it will display according to the resolution set in the nGlide program.

There's an old native port btw. You'll have to jump through some hoops to make it work on a current Linux tho. But it sorta works.

"There's an old native port" ??? Would you care to elaborate on this a little more? xD
I finally figured out how to make "default OpenGL" work inside WINE, posted a new thread about it:
(no patches or external files needed)
https://www.gog.com/forum/sin_gold/linux_wine_finally_made_opengl_work

Well, you won't need wine to run it that is. The catch is what you will need is to poke around quite a bit to get it to work. Still worth it IMO. However if you're not comfortable enough with your Linux-fu I'd imagine it kinda gets too involved.

If still interested https://github.com/liflg/sin_1.10-english_x86

Oh and I almost forgot - you'll need to get a hold of the original Linux disc for all this to work))) The resource above only provides some support thingies to fire it up on a modern distro... the game was ported around the time it was originally released after all... Needless to say you can grab the image at a decent b*ttorrent tracker...

Hello there
I hope this helps
https://www.gog.com/forum/sin_gold/how_to_run_sin_gold_on_linux_playonlinux_with_default_opengl