I had the unpleasant experience to find that SOR4 did not work anymore on linux. Console just shows "Running Street of Rage 4..." and return to prompt immediately.

Fortunately logs for the game are pretty explicit (in ~/.local/share/Streets\ of\ Rage\ 4\ Save\ and\ Config/) and show that the game could not load a wrapper for GOG Galaxy (called libGogGalaxyGCWrapper.so).

Solution was to edit the start.sh and replace the line
./"SOR4"
by
LD_PRELOAD=lib64/libGogGalaxyGCWrapper.so ./"SOR4"

Hope this can help.

Awesome information. Thank you for sharing~