In the SF/Fantasy cross Apprentice Adept series by Piers Anthony, the main character is a proficient player of the science realm's "Game". Two people face off at a game console. There, one player chooses one of four categories: 1. PHYSICAL, 2. MENTAL, 3. CHANCE, or 4. ARTS. The other player chooses among A. NAKED, B. TOOL, C. MACHINE, or D. ANIMAL. (Naked means unassisted by external tools.) Once the grid is completed, players continue on subgrids until they select a particular game to play. They then proceed to play that game.
Obviously a similar real world game would either require vast amounts of resources, or be modified to be more of a board-game style, thereby having to change the first 8 categories to be something doable in a living room. However, the strategy and ability to gauge your opponent's strengths and weaknesses, I feel, is the key point - as mentioned in the book, the ability to do well at the grid is often more important than a wide range of abilities in the possible resultant activities.
Are there any real-world games that mimic this?