What game(s) does Michael play in Mind Field S2E4?

Other answers are close, but lack a primary source. Michael Stevens (vsauce) himself responded in this Reddit thread, saying:

The footage on the screens is from a game called Star Citizen. However, FUN FACT: that footage is just placed on top of the screens in post. I was actually playing League of Legends, but in the end, LoL wouldn't give us permission to show their game or mention its name. Which game you play doesn't matter, though. It's been found that any 3D game can lead to noticeable results -- but not 2D games like platformers.

LoL was recommended by the researchers at UC Irvine. They've found that 2D platform games lead to a lower effect, but this is still a really new area of study. There's a lot more to test, experiment with, and learn.

It looks like he's playing Everspace 2

There's bits of various different game trailers and stock footage in there that the producers used to artificically replace the actual game he was playing. In actual fact, he was playing League of Legends, but they had to remove that footage for legal reasons. I noticed that this was one of the trailers used, but there are others.