How do I fix it? Please do step by step instructions.

It looks like the data files for the game are not in the same place as the DarkPlaces engine files so it cannot find them. DarkPlaces and other source ports, such as Quakespasm, should provide step by step installation instructions within a text file or on their official web pages.

Meaning you need to check that folder ID1 is present in your Quake (Darkplaces) folder, these files should be present there:
- PAK0.PAK (18,689,235 bytes)
- PAK1.PAK (34,257,856 bytes)
- autoexec.cfg (not really needed)
- config.cfg (shouldn't be a show stopper either)

If it's really there and you still can't run Darkplaces from that folder than download the latest version and copy files to that same folder again and tell us what you see.
https://icculus.org/twilight/darkplaces/download.html

Step by step for vanilla Quake (GLQuake) in Windows

1. Install Quake (e.g. C:/Games/Quake), select create shortcuts for convenience

2. Edit 3 shortcuts (Quake, Scourge of Armagon, Dissolution of Eternity), add this command line in target " -width 1920 -height 1080 -bpp 32"

example (see attached):
C:\GAMES\Quake\Glquake.exe -width 1920 -height 1080 -bpp 32
C:\GAMES\Quake\Glquake.exe -game hipnotic -width 1920 -height 1080 -bpp 32
C:\GAMES\Quake\Glquake.exe -game rogue -width 1920 -height 1080 -bpp 32

I highly recommend the next step as well:
3. update old GLQuake 0.95 (from GOG installer) to the latest GLQuake 0.98a, download respective .zip archive (098alpha.zip) and unpack its contents into main Quake folder and you're good to go.

link to one of repositories (there is nothing illegal here):
http://www.quaketerminus.com/exe.shtml

Oh no, this is in MINT.

Okay, if I click on the "Quake (software mode)" icon I can sorta get quake start. But it is low res, if I switch it to high res it slows down badly, and there is no sound. How do I fix that? I think this starts it directly in dosbox.

Quake software renderer (both DOS and WinQuake) are not designed to be run under Linux. Software renderer can't produce many effects and it has performance issues on high resolutions, moreover you will have a ton of problems with trying to make it work properly, lastly running DOS Quake in Full HD under DOSBox is just crazy. GLQuake was never designed for Linux either but at least it was patched and upgraded by John Fitzgibbons to FitzQuake and after some years by another team to Quakespasm, that's why all you need to do is to know how to handle Linux MINT libraries.