Credit to Deleterium's protondb report - that's what got mine to work. If first installing the game:

Install d3dcompiler_43, d3dcompiler_47, d3dx11_43 with protontricks Launch the game. Get a black window for the 'new' launcher that does not work. Copy the simple template file 'options.lua' from https://github.com/deleterium/dcs_on_linux to your folder /home/you/.local/share/steamapps/compatdata/223750/pfx/drive_c/users/steamuser/Saved Games/DCS/Config/options.lua Launch the game. It shall open in a small window. Go the the options (gear icon in top) and select manually your screen resolution and maybe try other configurations.