Automated testing is hard to justify for games because you are not simply finishing features and moving on. You are constantly experimenting. Throwing out features and ideas and reworking them is part of the creative process. Automated testing adds overhead to iteration and isn't free, so you have to be very selective. At the end of the day it is more important for the game to be fun than it is stable.
Though there are games where the fun has been proven, and it's important to be able to iterate fast without breaking what's already there. There's a great 2016 blog post from Riot on how they test LoL:
