System Shock: Classic, which comes with System Shock: Enhanced Edition on Steam, does have a Linux version. The Windows and Linux versions of the game are actually just the original DOS game packaged with, respectively, the Windows and Linux versions of DOSBox.

Proton seems to have no trouble running the Windows version, so it's an option for those who have problems with the Linux version. Running a DOS game in the Windows version of DOSBox on Linux using Proton is a bit convoluted, and might not be the best way to enjoy the game, but it does work. The only issue I experienced while running the Windows version with Proton is that the Steam Overlay doesn't work.

To be fair, the Steam Overlay doesn't work out of the box with the Linux version either, so I think it's just a DOSBox issue. Additionally, the DOSBox included with the Linux version of the game tends to mess with my display settings, mirroring my two monitors when the game starts in fullscreen mode. I was able to fix all of these issues in the Linux version by replacing the included DOSBox executable with dosbox-staging (https://github.com/dosbox-staging/dosbox-staging).

The Steam Overlay issue can also be fixed for the Windows version by running it with Boxtron (https://github.com/dreamer/boxtron), a compatibility tool which swaps out Windows DOSBox for Linux DOSBox, but I don't recommend it for this particular game. The use of Boxtron, with no further manual configuration, broke the music for me and seemed to cause performance issues. Rather than using Boxtron to configure Linux DOSBox to run the Windows version of the game, you might as well just run the Linux version (preferably with dosbox-staging).