Winning conditions don't necessarily need to be genre-derived. Here's an example off the top of my head. The winner is the player who builds from ace to king to subquental order. Like in Solitaire, cards may be stacked in order beginning with the ace, then the 2, then the 3. For a fighting series, that growth could be a single character powering up. For a romance series, the cards could represent the stages if a relationship. In a mystery or horror, it could tell the series of sequence of events in a story.
The above, by the way, us NOT a GOOD mechanic. It's pretty bad. I'm just throwing it out as an example.
And yes, I do have the rough draft rules of a card game I created for Alien Fiction. Mine is not well suited for any other series, and I'm not happy wuth it myself, but that's a topic for another time.