[ERROR] SteamException: [S_API FAIL] SteamAPI_Init() failed

The error says that the Steam API could not be initialized The server then shuts down (because it can't run or authenticate players without Steam unfortunately)...

Usually this indicates that for some reason Steam or the Steam dlls could not be loaded... but I must admit I haven't seen that happening on Windows before (usually this happens on Linux if a wrong library path was specified)...

In rare cases it may also happen if Steam is down, but then it usually works if you try again later.

It may also be caused if the server can't bind to the port (although that's probably unlikely)...

Do you use SteamCMD, or the the actual Steam client running? If the Steam client is running, please restart it and try again. Otherwise, if possible, maybe try to restart the server machine and see if the issue still persists.