I'm on Arch+XFCE (I have never seen another game exhibit this behavior).
To be clear, esc will still open the menu but mouse input still didn't work (even on restart of game). Editing the settings file to revert back to fullscreen fixed it perfectly, though.
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You're right, I tested it on Cinnamon and it worked fine. Further testing in XFCE, I can get it working if I unmaximize the game and manually shrink the window. Probably forces something to recalculate properly. (maximizing again re-breaks it)
My guess is my setup is an edge-case that you don't have accounted for. Specifically, a maximized window that is native sized (1920x1080) due to XFCE window manager tweaks (accessibility>hide title of windows when maximized\*). I'm not sure why it'd cause this problem, unless maybe some differing technical requirement for fullscreen vs windowed (+trying to detect fullscreen via window resolution).
EDIT: It still occurs when maximized with the mentioned tweaks disabled, so it does not need to be exactly native-sized. If I also set theme to RedmondXP it works fine when maximized (funnily enough, if I un-maximized it went to the previous size which did cause the issue again, and manually scaling it larger-than-native did not cause the issue so this is very odd)
\*=Also the frame setting that is required, though I use a window manager theme that is extremely minimal, almost frameless. Plus an auto-hide panel, so even with those tweaks disabled on my system a maximized window has content at 1920x1068.