While I've never had one that I was the personal staff of, a lot of my friends have. And I can see the appeal. So, instead of my own cat, I live vicariously through games that involve them. One such game is up on Kickstarter now. It's called Last Cat Standing.
In the game, players will have various cats in front of them and will get in battles with other player's cats. When attacking, a player will roll a number of dice equal to their cat card, plus an attack card they play. Meanwhile, the defender will pick one of their cats to defend with, and can also play a defensive card from their hand. Both players roll their dice. The losing player must lose one of their cats, as well as lives equal to the number on said cat. You have nine lives, total (as one would expect). When you lose your last life, you're out. As one would expect, the object of Last Cat Standing is to be the last cat standing.
The Kickstarter campaign is up and running now. It's set to go for another 17 days.