Has anyone managed to get this to work on the Deck? I've been struggling with getting the FMVs to play.

This is a bit odd. I had a first install (I guess installed via Lutris) which ran without any issues. FMVs ran well.
Now on my Deck it runs well too but FMVs do not. I should take a look into this older install, if I can see any difference.

My Deck install however is easy, just installed normally with Heroic. I can start it directly from there or add it via BoilR to Steam and do it over there.

The only thing I just can't get to working is the Direct3D11 Renderer for this engine. It's the same that can be used for Unreal, Undying, some more and Star Trek DS9 - The Fallen which doesn't want to start with this renderer neither. The worst part is, the HD Texture Pack for WoT only works with this renderer. To find it, just search for "unreal d3d11 renderer moddb".

I hope my tech support request on the linux_gaming subreddit can bring some help over this. Then I will add it here.

Did you have any luck? When I try, I get as far as the main menu, but the "The Wheel of Time" logo splash stays up. I can hear the intro and menu sounds, but the screen never changes.

Hey, yes I've managed to make it work. Turns out GOG already packs a ddraw wrapper with the game that allows for FMVs to play. All one needs to do is to force wine to use the bundled dll instead of the default system one.

WINEDLLOVERRIDES="ddraw=n,b"

or

WINEDLLOVERRIDES="ddraw=n,b" %command% if using proton instead of wine.

Credit goes to this good user here - https://www.gog.com/forum/the_wheel_of_time/the_wheel_of_time_in_wine_linux/post9