Shipped 17 games, several AAA games with no automated testing. Not saying that was good only that it happened and so is at least some evidence that automated testing is not essential.

The problem with automated testing in games is most of it will be content specific and the content changes multiple times a day. A product like say GTA5 has 20-30 programmers and 300 artists and game designers. Those 300 artists and game designers are adding new content and or changing old constantly. Often they also use a scripting language or a blueprint like visual language to setup in-game logic like "open blue door if player has blue key". There's just too much to test. Every day 1000s of tests would have to be re-written because some boxes, doors, etc were moved .5 units to the left.

There isn't zero value in automated testing (see above) but my experience with testing on a large project, Chrome, was that it really slowed down my velocity. Easily by much more than 50%. Of course Chrome is a platform and absolutely needs the tests IMO. I think a game engine would benefit from lots of automated tests. The game itself though it gets harder to figure out where the balance is between automated testing and manual testing.

As others pointed out as well big teams, like an OS team or a browser team often have dedicated staff to setup and maintain a testing infrastructure. Game teams rarely have this. Maybe they should but few games are given the budget.