Password accessed games allows the Premium game creator to have more control within the game.
The password also serves to provide some privacy, to restrict the game to a limited circle of friends.
Sometimes the game creator wishes to open the game to the public, but if it is not publicly listed, it can slowly lose visibility on the forum, Twitter, Facebook, Google+, or Reddit.
I suggest that password accessed games should be listed publicly with all the other User Created Games.
The Premium game creator can then decide whether to share the password publicly in the game description.