How overloaded with apps is the device?
Did you leave enough 'breathing room' for whatever game you are playing?
A good rule of thumb seems to be to keep your internal memory at or below 70% of its capacity.
https://f-droid.org/en/packages/com.kgurgul.cpuinfo/
Any game that requires a substantial amount of RAM is going to cause heat to be produced.
The way you hold the device should allow air to get to the hottest part that you can feel.
Giving the device a break once in a while is a good idea, too.
You actually could hold the phone in front of a small fan while you play. It's actually kind of nice during the summer.