Is it normal for the battery to heat up while playing games?

It's not necessarily the battery that's heating up but your phone itself due to the load on the processor because of the game. This is normal and to be expected and can vary by app/game.

In addition to what adfelkopf correctly pointed out, take a look at this support article too:--> If your iPhone, iPad, or iPod touch gets too hot or too cold - Apple Support

Regards

Giulio