From what I know the game works fine on at least two different machines.
The script for rotation of the player/camera utilizes Unity's built in Input "Mouse X" and "Mouse Y", which detect whenever mouse has been moved in X/Y axis. The inputs are originally set to mouse movements, but can be changed in the launcher before starting the game - if you changed inputs before launching the game it might be a problem. If not, then I can only speculate. Maybe it has to do with the mouse itself and it's drivers.
Thanks for checking the game out, though.