When you make a game, you’re kind of creating this unfulfilled contract between you (the designer) and your intended players. When they pick up the game to play it, they are accepting the implied contract, which is that you the designer have created for them a play experience they the players will enjoy. Some games are more open-ended in their design, however: they allow the players some control over the mechanics and rules of the game so that the player join the original designer and become “further designers”. This phenomenon happens even in games that don’t have such provisions for game control on the part of the players: after all, house rules and variants are in fact this very thing, players designing a “better” game.
In Magic, the creation of a “Cube,” or engineering a subset of cards from which to draft and play together, is one way that people have found to put their player-design stamp on their own play experiences. I made a Cube, in fact, and did so in a way that tailored the full experience of Magic down to a specific experience I enjoyed (playing with lots of “when you play this” effects). Two things I noticed, however: (1) the idea of the Cube I made was more exciting than the Cube itself, but only I had this feeling about it, and (2) I really did feel like the “game designer” when people played with my Cube.
I just played with and enjoyed a different Cube today, Adam Styborski’s Pauper Cube, which had a totally different experience associated with it. I think that player-design is an important tool to use to help a particular audience find the “best” game for them using a more generalized game as a template. Since the necessities of economy generally mean that a produced game has to appeal to a broad audience, player-design helps games reach the more niche (and more compelling) audience that wants to have some ownership of the game itself.