A game can’t damage your MacBook. It may seem like it does, though. As you play, the load on your Mac increases, which can lead to more vigorous work of the cooling fans and a rise in the temperature of the processor. The performance may drop, but it will restore as soon as your computer cools off — no permanent damage is done.
MacBook Pro is equipped with sensors that track all parameters of your device. You can turn it off as soon as it gets too hot, which can corrupt its work. If you regularly use your Mac to its full capacity, we recommend using a cooling mat or a laptop stand to further cool it down.