Hi Bullfright,
There could be several reasons why games may not work or even load on a Chromebook, but works like a charm on an iPhone:
OS Compatibility: There are games that may only work with specific operating systems, such as iOS, and may not work on Chrome OS. Since they are completely different operating systems, their framework works really differently.
Browser compatibility: If the game is a browser base then you must consider that it may not be compatible with the Chrome browser, and may only work on specific browsers such as iOS browsers such as Safari.
Flash Player: This is very important. There are games that are only accessible if you have Adobe Flash Player installed, which is sadly not supported by Chrome OS.
System Requirements: The game may have certain system requirements that are not met by the Chromebook, such as required specifications of processor, graphics card, or amount of RAM.
Internet connection: This is a lesser common issue that might also be the cause of your games not running on a specific device. Take a chance by restarting your router or modem, or testing your connection speed to see if this is the issue.
You can also try to contact the game developer on the website specified on the game. They will give you the exact troubleshooting required to run that game especially if they are working before on that device but just suddenly stops working.
Best of luck!