So I have been seeing some people having trouble with COD4X and Steamplay on Linux where when launching COD4X, it complains about some missing DLLs and then attempts to load a previous version (1.7 in my case)
I dug around and found out that the DLLs that COD4X requires are placed in a folder called "cod4x_0??" within %APPDATA%/Local/CallofDuty4MW/bin/ (Or "SomeDriveLetter:/Users/*Your User*/AppData/Local/CallofDuty4MW/bin/), at least on Windows. After you use the install script, they are placed in a similar path in whatever wine prefix you ran the installer under. I had to dig around quite a bit to find the needed folder. Once found, copy the DLL folder into this path: *YourWinePrefix*/drive_c/users/*YourUser*/Local Settings/Application Data/CallofDuty4MW/bin/.
If you need an explanation for how Proton wine prefixes work: https://github.com/ValveSoftware/Proton/wiki/Proton-FAQ#how-does-proton-manage-wine-prefixes
This worked for me and allowed COD4X to start and at least talk to the master server to get listings. There is still another issue I'm trying to work out where COD4X can't connect to any servers as it claims Steam is not running. Whatever systems COD4X has to talk with steam do not work with Proton clearly.
More info can also be found here: https://cod4x.me/index.php?/forums/topic/2810-linux-steam-play/