Not a full distro but perhaps take a look at the Games on Whales project?
You could do a minimal Arch install then it on top of that.
Or maybe since the whole setup will live on docker, maybe some flavor of immutable distro? I use and enjoy OpenSuse MicroOS






Man, that trailer looks rough.
Unity always had (the often underserved) reputation of being an engine for crappy free mobile games, and what they have in that trailer looks exactly like the junk flooding the Play Store.
Geez, if you’re gonna make a trailer for your new product at least try making it look good.