Is that where players line up on the wall and try to avoid being hit by tennis balls being thrown at them like target practice and you have to catch the ball to stop being the target?
No, I think you're talking about dodgeball. In the Eton Wall Game two teams basically form a scrum over a ball placed against a wall and then try to drive each other laterally along the wall toward the end of it. The reason it's so violent is that, if you happen to be the player against the wall, you lose most of your skin. You're also allowed to push your fists into an oponents face (though not actually punch), hook legs and so forth.

What was the game?
I don't think anyone really knows. There are just lots of depictions of people dribbling balls in early Chinese art.

As I reach for the Post button I find myself wondering if the phrase "Dribbling Balls" will get passed the profanity filter.