If you use a Linux distro as rtcvb32 suggested, you need to go to
https://www.gog.com/account and click on the game you want. Then, download the installer files from the part that says "DOWNLOAD OFFLINE BACKUP INSTALLERS",
and not from the big blue button right above.
If you're using a Linux distro and this distro is compatible with Wine, you could probably play both Linux and Windows games in your device.
If you can't install Linux games, there's still a chance the game itself works. To extract the game files without installing, use a tool such as unzip to extract the files from the .sh installer (such installer is just a fancy ZIP file).
For Windows games, it should be possible to install them normally by using Wine (on a terminal session, type "wine name-of-the-installer.exe" without quotation marks, then press enter to run).
Now, if it uses a stock OS, then sadly I can't help much, as I never used ChromeOS nor have I gone after any info.