First some info, I have gotten Clear Sky and Call of Pripyat to work with normal Wine, using Winetricks to install corefonts, d3dx9, gdiplus, and tahoma, and launching the games with the settings launcher instead of the normal shortcut. I'm on Ubuntu MATE 15.10. I use the installers with the /nogui option so that they don't freeze at the end.

OK, so that works fine with the other two, but in SoC, when I launch the installer with nogui, I get a window "Runtime error (at 195:57): Could not call proc." If I ignore the windows (the same message pops up every time I change pages in the installer) then it installs way too fast and none of the folders in the SoC folder are present except for the "Localization" folder, as if it's ignoring the .bin file.

Updated to Wine 1.8, ran without GUI, now it gets "Runtime Error (at 68:445)", but it works, so that's that. Thanks.

I'm getting this exact same error. The game seems installed just fine, but when launching in PlayOnLinux I'm getting errors about missing DLL's:

xrSounds.dll
xrLUA.dll
xrCDB.dll
xrCore.dll
Needed by - C:\\GOG Games\\S.T.A.L.K.E.R. Shadow of Chernobyl\\bin\\dedicated\\XR_3DA.exe

I never get the opening movies or menu to load.
Are you experiencing these errors after launching?

I can actually run the game right after installer is finished by clicking "Launch", but after creating the shortcut, it errors the above...