I get the exact same error you're getting. I own a GTX 660.
However, setting PROTON_FORCE_LARGE_ADDRESS_AWARE=1 fixed it for me (I'm running the Steam version of the game). The warnings about Unknown format encountered are still there, though.
PROTON_FORCE_LARGE_ADDRESS_AWARE=1`x1 2020-02PROTON_FORCE_LARGE_ADDRESS_AWARE=1x1 2020-02WINE_LARGE_ADDRESS_AWARE=1x1 2020-02
When starting The walking dead season 1 it loads up to "loading...." and crashes afterwards. I do have other d3d9 games that work correctly with dxvk/d9vk and it works with the wine opengl based implementation. It might be related to the issue here: https://github.com/doitsujin/dxvk/issues/1380.
If an apitrace would be useful I will provide one later.
Software information
Walking Dead Season 1 (GOG version) without settings
System information
Log files
terminal.txt
EDIT: I don't completely understand why it would need more than 2gigs of ram in either gpu or cpu memory, but it seems like that is indeed what it needs. I don't know enough about dxvk and wine to say anything about it though, so don't take my word for it. guihkx is correct and installing a wine build with support for forcing LARGE_ADDRESS_AWARE (I used the 32 bit proton build here https://github.com/Kron4ek/Wine-Builds) and setting PROTON_FORCE_LARGE_ADDRESS_AWARE=1 or WINE_LARGE_ADDRESS_AWARE=1 will fix it. The LARGE_ADDRESS_AWARE patch is not implemented upstream yet as far as I can see, but it seems like that would be a fix for walking dead season 1 + dxvk compatibility with wine vanilla.