I tested this on proton 8, and the movies now play. However there is a bug in that happens at the end or whenever the you try to en the movie. The game well freeze, and become totally unresponsive and the only thing you can do is kill the process. This happens in wine 9 staging as of my testing. I managed I have submitted a fix for this upstream here. I also tested this fix with bleeding edge of proton and it was working fine the movies were able to complete. I found that the issue happened because of a deadlock when ending the movie. The deadlock happens in quartz.

Here are some relevant logs highlighting the issue (please don't mind my debug traces). As you can see the VideoWindow_put_Visible runs and gets the lock for the filter_graph object. This leads to show_window getting called and later on set_window_pos (this is all while holding the lock for the graph). Further set_window_pos calls apply_window_pos which invalidates the DCE, likely causing a WM_PAINT message being send, which end up in VideoWindow_NotifyOwnerMessage (WM_PAINT = 0xf) . But VideoWindow_NotifyOwnerMessage can't finish because it doesn't have the lock, VideoWindow_put_Visible has the lock. Later on VideoWindow_put_Visible send a new message WM_ERASEBKND this never returns as it is likely waiting for WM_PAINT to finish, thus we end up with a deadlock scenario.
You can find logs here

Movies currently play perfectly on desktop with SteamOS 3.6.6/Proton 9.0-2 on OLED Deck, while the video stream stays black and only audio plays within Gamescope-session.

ENABLE_GAMESCOPE_WSI=0 %command% fixes the issue, as reported by two OLED Deck owners I helped with troubleshooting this on SteamOS' Preview branch. I can try and grab some Gamescope and Proton logs from my own Deck later, but it should be relatively easy to repro since it happens with the intro movie or if you fast forward until you reach other video (plus - no nsfw stuff, yay! 🐸)

Proton experimental, WSI on, black intro video screen w/ audio playing:
steam-857450-wsi-on.log

Proton experimental, WSI off, perfect video + audio:
steam-857450-wsi-off.log

Gamescope-session log has nothing interesting.

Tested on my OLED Deck, Gamescope 3.14.22, Fedora 40

EDIT: re-tested on SteamOS 3.6.20 with Proton Experimental and the issue no longer occurs