You know how the winner of Netrunner Worlds gets to help create/design a card, which other people can later use in their own decks? Think about something like that, but on a larger scale and in a less direct way.
Winners of tournaments in L5R CCG could make votes/decisions about things that could happen to main characters in the game's overall story meta. Different cycles of cards had different major conflicts or events going on, and outcomes for those events were determined by the results of tournaments. So for example, maybe there's a war going on between two major clans/factions and their allies, and the outcome of which side wins is determined by which factions won more tournaments or special events being held during that event. The winning side might get a new or improved card released during a later set, while the losing side might have some other negative or intriguing consequences for their own cards.
Imagine, for example, if Mumbad Cycle and the results of the election were determined by results at GNKs or store championships during that season (e.g., maybe the faction with the most 1st place wins gets a special hardware/event that comes out in a later cycle). It's a little harder to apply to Netrunner because the cards are already thematically centered around specific locations, but it would be kind of like that.