Last time I used the Facebook API they didn't provide any multiplayer or gameplay functionality. I'm pretty sure you have to write that yourself.
You can still leverage the Facebook API to publish scores/achievements and find friends of a user. Eg. You can get the user-names, profile pictures from FB and also use the Facebook API to post something on the users wall to draw more attention to your game. Achievements and scores are also a part of the Facebook API now.
The tutorial you followed is pretty much all there is to it. Facebook gives you the "social" data of users, everything else is up to you.
To find friends for a multi-player game (as your question suggests), you could use the FB API to find the friends of a user which are currently online and send a request. Your server-application will have to handle the creation of a multi-player session when requests are being accepted.