My opinionated version is that you should bail out on games and focus on AI/ML, then try to get into the best grad school you can and get really good at difficult things that other people can't do (even better, things that they can't do and don't want to do). Games fail that test because too many people want to work on them.

Becoming a good software engineer seems to come from working with people with good taste (on real projects). In my experience I haven't met anyone who learned to be a good SE from university (it may be possible, but I doubt it would happen at a mediocre university).