By default BAF is using it's own prefix and cannot find Arma 2: Operation Arrowhead, which is required. The A2:OA prefix can be forced with launch options: "STEAM_COMPAT_DATA_PATH=/home/(USERNAME)/.local/share/Steam/steamapps/compatdata/33930 %command%". Before running A2:OA needs to be started first, and game key edited manually to registry [Software\Wow6432Node\bohemia interactive studio\arma 2 oa] to work around bug in steam, see https://github.com/ValveSoftware/Proton/issues/1308#issuecomment-481728178 for details. After these steps game works fine when selecting Play in Arma 2:BAF, however starting Arma 2: Operation Arrowhead removes the registry key and it needs to be added again.