Sounds like you could use AJAX for this:
The ajax could make post requests to a php file that checks a database for: register/login/authentication/user (game) details.
Also, for the login you could use the google/facebook plugins do to logins/authentication of user, even save and retrieve scores for the respective login systems.
Scores would be related to the respective plugins/login systems too. However, if you store and retrieve scores from your own database, then the scoreboard could be universal, regardless of login system.
As for multiple games, any uploaded game is able to get loaded on a unlimited amount of end users. (with or without logged in system)
You could add checks by means of events in a game to see if a user is logged in, and then allow or disallow access.