Hi tanvir39,
When you're playing your game, how are you holding the device? Is it possible that during your game play you are using a gesture that closes the game and returns you to the Home Screen?
Gesture, swipe, and press to navigate your iPhone 13 and other Face ID models - Apple Support
Use gestures to get around
To create a continuous surface, the Home button has been replaced with new ways to navigate.
Unlock and get to the Home Screen
* To unlock your iPhone with Face ID.
1. Glance at your iPhone
2. Swipe up from the bottom of the Lock Screen. Or if your iPhone is on a table or other flat surface, you can raise it or tap it to wake it.
* To go to the Home Screen at any time, swipe up from the bottom edge of the screen.

If the issue continues without taking the gestures above, then ensure iOS is updated, check for updates to the app, and reach out to the app developer to further troubleshoot. Check out those suggestions here: If an app on your iPhone or iPad stops responding, closes unexpectedly, or won’t open - Apple Support
Kind regards.