Hello, mfdavid.
If the controller is working on some games on your Mac, but not all, that tells us that the Mac and controller are probably physically okay. Just in case though, this Xbox support article might help: Troubleshoot your Xbox Wireless Controller.
Reaching out to the individual game manufacturers may also be a good idea, as they would have the best knowledge as to what issues can arise with using a controller with your Mac.
To narrow down possible issues on the Mac that might be causing this, you can try testing to see when this behavior occurs. First, put your Mac into safe mode and test. Booting into safe mode will disable any startup and login items from automatically opening, which can help us to isolate the source of the issue further. When you do this, you’ll see some unusual behavior from the display; this is to be expected. Please follow the steps in this article: How to use safe mode on your Mac.
Next, you can check to see if this behavior persists in a second user account on your Mac. Please follow these steps to make a test account that can be deleted later: Set up users, guests, and groups on Mac.
Let us know if we can help with anything else at all or if this doesn't settle your issue. Thanks and have a fabulous day!