The gameplay fully works, but the videos (FMVs) aren't working at all: they show one frame per several seconds. You can clearly see the interlacing in the frames.

Specs: Proton 3.7-3, Ubuntu 18.04, NVIDIA Corporation G94GL [Quadro FX 1800] (rev a1)
Full specs: https://gist.github.com/adrianlshaw/13b21eae4d9ad3c6c79474396110feed
Same result on my end. See video.
Gamepad support: Xbox one gamepad tested. Not working.
HARDWARE: Proton 3.7-4 beta, Antergos XFCE, NVIDIA GTX 1050 TI. Driver 396.54-5.
Skimming through the community forum it looks like the windows version suffer from the same problem depending on drivers and Windows version.
Actually, testing with vanilla Wine 3.14, videos play fine. Maybe the problem in Proton have something to do with the full screen stretching it uses instead of switching resolution?
if you use -interline as a launch option that seems to fix the cut scene issue. (At least it does for me and reported for others)
Confirmed, everything works fine using Wine 3.14. It seems the problem with the cutscenes is proton only.
I can confirm that on a Macbook Air 2013 with 8GB RAM, Intel Core i5-4250U with an integrated graphic card Intel HD 5000, the videos aren't working fine. Although, with -interline I can watch the videos almost OK, there's a strange effect that even while on-play it shows lines (I guess it's the interline) and the definition isn't as great as it was while without -interline. The gameplay seems to be great though.
This method works as an alternative to the "-interline" launch option:
https://github.com/ValveSoftware/Proton/issues/2106#issuecomment-497254074
The upside is no horizontal black lines. The downside is it runs at a much smaller resolution.
This is still an issue with Proton 4.2.9.
Also, the game works fine with Wine Staging 4.11.
Most helpful comment
if you use -interline as a launch option that seems to fix the cut scene issue. (At least it does for me and reported for others)