"C:\ProgramData\FAForever\bin\ForgedAlliance.exe" (in directory "C:\ProgramData\FAForever\bin"):
CreateProcess error=2, The system cannot find the file specified

looks like the (FAF) ForgedAlliance.exe is missing in C:\ProgramData\FAForever\bin\

Please deinstall FAForever client. Delete the Folder C:\ProgramData\FAForever\ manually Don't skip no 2. ! reinstall FAForever (make sure your antivirus is off and not interfering with the download/install) Start FAF client and host a game

Because you did not post the full log i can't see if the ForgedAlliance.exe was downloaded from the client or not.
So from what i can see its maybe your antivirus programm that was deleting the ForgedAlliance.exe