Can I ask how exactly are you trying to start the game? Are you launching it via Origin app directly?
If not, I would recommend to open your Origin app first and try to launch it from your games library to see if this error message will still appear.
I am having the same problem. I open Origin go to my games and launch BF3 sign in and then switch to BF4 enter favorites and attempt to play a match. Popup says unknown game enter game key . I enter the key and it will not accept.