Mark "Buckshot Roulette.x86_64" as executable and double-click it to launch. Or in console: chmod a+x "Buckshot Roulette.x86_64" && ./"Buckshot Roulette.x86_64"
If it doesn't run you might be missing Vulkan libraries: sudo apt install libvulkan1
I took the time to play through this on Windows. This game is a real gem, extraordinary beautiful! I wish there was more to explore. I hope the Linux issues won't discourage you from publishing future games for multiple platforms. Keep up the good work!
However it seems to depend on the settings. The only setting I've checked that works without issues is 720p windowed with quality "OK". Higher resolutions, fullscreen or quality "BEST" gives me flickering or no picture at all.