Hello TexanInParis,
Let's use the steps below restart your iPad:
1. Press and hold either volume button and the top button until the power off slider appears.

2. Drag the slider, then wait 30 seconds for your device to turn off. If your device is frozen or unresponsive, force restart your device.
3. To turn your device back on, press and hold the top button until you see the Apple logo.
You can also find those steps in this resource: Restart your iPad Restarting can sometimes help address odd behaviors.
Should that still persist, how many games are exhibiting this behavior?
Are those games all up to date? How to manually update apps on your Apple device
Also, have you experienced this behavior with any apps that aren't games?
Let us know, and we'll keep moving forward from there based on those details.