Well, this is what I was thinking:
We would announce a tournament for a certain game for a certain day and state a time limit for potential contestants to enter(Perhaps even a limit on the number of contestants which would then require admission on a first-come, first-serve basis with a certain amount) Then the theoretical brackets and rounds etc. All the while the scores would be reported using the already established Challenge system and eventually an overall winner would emerge.
I don't really know about playing every single game, but that could be thought about also.
In response to cbwing0's question about challenge system(Seeing how I was the first to use it
) , you click on somone's name while in the arcade. This pulls up their statistics and in there is a link that you click to challenge that person. Then you pick the game you want to challenge them in. They will learn that they have been challenged upon entering the arcade. If they accept, they will play the game and get a score that is stored. Then the challenger will be notified and he/she will play the game and get a score. After both people play, the scores are displayed publicly in the challenge section. It's a lot easier than what I made it sound like, so just try it out.