In Genesis, players can invent their own games in one of two forms.
The first form takes place on a game board, with any variety of pieces the player chooses. Using simple scripting (writing rules for the game), players can create their own turn-based board games, like chess or checkers, or even invent their own.
The second form of game takes place within the world. Using a similar system of creating rules, players can script their own games. For example, to create capture the flag, you simply define where two flag bases lie, and a winning condition of two flags being in the same base. Additionally you define a rule that if a player tags another (or strikes another), they must return the flag to the base and then return back to their base. This might seem tricky to do, but if you have any knowledge of expert systems, you will realize that this is actually fairly simple.
The scripting system could even be used to place bets, or define other conditions that seriously affect the players (e.g. “Whoever wins this game of chess gets to execute the other person”).