I do things a bit differently.
not categorized = Early access game or yet to be categorised
beaten = Played enough to be fulfilled and/or the game is multiplayer (so cannot be completed)
completed = Story completed
I don’t care for achievements, so if I sorted my games in the site’s proposed style then the “completed” category would be very empty. I like to indicate to myself when I am finished with a game as opposed to letting an achievement list dictate that to me.