I think the #1 reason why games don't need a lot of automated testing is serialization, or rather the common lack of it in most game worlds. If the data gets corrupt, you can reset the game and all is well again. When the rare corner cases pop up, it's easy to play whack-a-mole with them, because they're all "shallow" in the sense of the game starting from a clean reset frequently, so you can usually reproduce the bug quickly.

Of course, if the game does need heavy-duty serialization of everything, all bugs are potentially deadly. And this is largely the case for the line-of-business, social, and productivity apps, because that data is considered mission-critical. Corruption is not OK, reverting to backups is to be avoided. When a game has that kind of requirement, things get a lot tougher - and so games have naturally evolved to favor minimizing the save data to nothing or a few stats.

And this is borne out by looking for contrapositives. There are two genres that have a history of tending to be buggy because of some form of long-term data corruption: Large-scope RPGs and turn-based strategy games. It's hard to reach the bugs in those games, so it's also hard to fix them.