App Inventor was not created with multiplayer apps in mind Leslie. However, there may be some creative ideas in the threads here :
https://groups.google.com/forum/#!searchin/mitappinventortest/multiplayer$20game
Games might be possible using Bluetooth clients / servers, eMailing chess moves back and forth, using sms texting to exchange moves etc. I do not expect this will be easy. There are plenty of games and puzzle ideas .. here are some of mine:
https://appinventorforfun.wordpress.com/tag/gamepuzzle/ These are single play games that might be adapted but I image it would be very difficult to adapt most of them. Your student might also google something like app inventor multiplayer games and come up with some ideas.
Also check the AI2 Gallery (the link is the Gallery menu item on the browser) and find many multiplayer (apparently) games listed ..most of these are probably using a single Android device..I have not looked) some might be two devices.

Regards,
Steve