As far as I know it won’t work on a chromebook :)
The reason is that the current version requires steam for stuff like the Puzzle DLC and Achievements. Since the itch.io version is not really selling a lot of copies, I instead offer to exchange it for a steam key after purchase if you want to upgrade to the newest version. Just forward your itch.io purchase confirmation to ~~~@~~~~~ (redacted) :)
Hope that makes sense!