It depends on your permissions and Linux install, but you can often just double-click or run via terminal. Depending on what other games you've run, you may still need to install some libraries. You'll be able to see error messages indicating what libs are missing if you try to run it via terminal. This can help with some of the common issues, especially the most common missing libs:
https://askubuntu.com/questions/348267/x86-file-not-executing
To my knowledge, chromebooks don't have a standard linux distro on them so they may not to be able to do that sorta thing. But it shouldn't be any tougher for this game than other Unity games.