All you have to do is beat the score above you on their game. If you do, post a score from another game as the score to beat.
Ex. Player 1: Beat my score on Scoregamites level 2 of 800 points. Player 2: I beat your score with a 950 score. Beat my score on Growbox lvl 8 of 990.
and the game will go on until nobody can beat somebody's score. The person with the unbeatable score is the winner of this game.