for some reason the mouse is not working in the linux version
Doesn't seem so - it neither works on Slackware64-current nor on openSUSE Leap 15.0, but I'll try with a Ubuntu Live CD tomorrow to be sure.
The problem is that the mouse cursor can't be moved - clicking seems to work fine, though, but that's obviously not enough to play an adventure game ;-) The log file doesn't seem to contain any relevant information about the problem.
This problem does not occur with Murdercide 2017 and Alluvium, though Blood Mechs also seems to be affected. Your other games which I've played already don't seem to support mouse input.
Oh very weird that murdercide/alluvium work and peridium doesn't. Hrmm. Could be the specific version of unity I used for that one, I know there were issues with one version with controllers being plugged in or something. I've rebuilt with a later version, so try it again (v1.4) and let me know if that works!