I'm no longer seeing any Proton specific issues with this game, so I'm closing this. All the videos are working now (tested with current Protion Experimental), the misaligned text in the game with 16:10 aspect ratio is apparently a problem on Windows too.
mfplat.dllx1 2019-05
Compatibility Report
System Information
Distro: Linux Mint 19.1 Tessa (64 bit)
GPU: Vega 56
Driver/LLVM version: Mesa 19.1.0-devel/9.0.0
Kernel version: 5.1.0-050100-lowlatency
Proton version: 4.2-3
I confirm:
Symptoms
The actual game works fine, but the startup logo videos are skipped and main menu background video does not play. This in no way affects the actual gameplay, as there are no videos or cut-scenes during the game.
media_info_startup.txt
media_info_menu.txt
steam-426310.log
system_info.txt
I found this in the log
167079.546:002c:002d:trace:module:process_attach (L"mfplat.dll",(nil)) - START#1464 The game appears to use mfplat.dll and the codecs are:
startup videos: MPEG-4, AVC + AAC
menu video: WMV, VC-1 + WMA
Note that text in the main menu is misaligned if using a 16:10 resolution, in 16:9 resolutions it looks OK. This however I believe to be a bug with the game and not proton.

Reproduction
Just launch the game