Unfortunately, it seems not all of the cutscenes have been transcoded for Steam's shader cache. The opening cutscene works, and I did see that at least one of the "oops you let a character die" cutscenes also works, but this is what I get before the first boss.
Cutscenes can be fixed with Protontricks, and maybe GE Proton can do it as well, but I was hoping all the cutscenes would "just work" now that I saw that the first one was working. I suppose we should rely on Valve remotely transcoding videos for us anyway.