When I'm playing a game on my iPhone it gets really hot.

If the phone only gets hot when you are playing certain games, then you know that the games are causing the issue. Contact the support folks for the games to see if there are any recent updates that you can install.

If the phone is getting hot in normal general use, that is another matter that may require a visit to an Apple Store or Apple Service outlet.

Check the Battery Health of the phone. Settings > Battery > Battery Health. If the health is under 80%, the phone needs a battery replacement.

Phones will get warm or even hot under heavy processor load, which can include gaming. As long as the phone isn't too hot to hold, I wouldn't worry too much about it. Just be sure to take some breaks to let it cool off (the breaks are good for your wellbeing, too).

If it's too hot to hold, make arrangments to have it evaluated by Apple:

Genius Bar Reservation and Apple Support Options - Apple