We do a similar game Called Chocolate Ping Pong, each cup has a chocolate in it and the player has 3 turns to get the Ping Pong ball in the cups and if successful get that Chocolate, they all love it.
I use this in summer to encourage residents to drink extra fluids. I don't do opposing sides, just one pyramid of cups and each resident takes turns in tossing a ball ( or bouncing on the table) into the cups.
I tried with empty cups however they were easily pushed over with the ball. If you only fill a cup quarter of the way it shouldn't make too much mess at all. I didn't have an issue mess wise with the liquard.