I think it would be a good idea if when you log on, there's something similiar to the "XX games waiting" which says "XX games completed". These games would only be those which have not been viewed in their completed state by the player.
If u click one time on 'my games' you can see all completed games which you haven't archived. And if you look to all games when you archive them, you see all games which have not been viewed in their completed state...