too much chess
From a different angle, how about a multi-game tournament where the games are nested?
To explain what I mean by nested, here is an example:
Back in high school, some people played a game of Risk, where each battle was decided by the result of a game of Stratego, with the Stratego game being handicapped somehow with respect to the forces in the Risk battle that initiated it.
How about a tournament where the large-scale game is something like Risk/Diplomacy, i.e., multiple factions maneuvering armies to battle over control of the world/Europe, but each battle is settled by a game of Go, where the Go game is handicapped according to the sizes of the forces involved.