Ok - I found the source of the cursor drift.
There is a know unity bug on some browser that causes this issue.
In order to solve it i needed to disable cursor locking.
Now you will be able to drag your cursor outside the game screen.
This also means that the game can use the hardware cursor now so it should also help a bit with cursor sensitivities issues.
I uploaded new build. There indeed was a bug with the "...what I did to the captain" line. I also tinkered around with the cursor - added some extra smoothing that might help with a drift. I would appreciate if someone with that issue could give the game another try and let me know if it helped.
 "Tales From The Arcade: Starship Murder"){kind=icon}