It's been a while but your nice hosts come up with a game in roughly an hour, this one for the cat owners out there! After a fairly long meta, we get into the mind of a cat and design a competitive game for them to play.
At least two cats
A cat toy shaped like a die with a treat inside
List of activities the die points to
Pick an end date for when the game stops (can be arbitrary).
Give the cats the cat toy shaped like a die, they will roll the die and leave it eventually, and this determines the next activity for the human to set up. Once the die decides what the next activity is, the human sets it up based on a chart. Once the task is completed and cats are awarded points, repeat the die roll and do the next activity until the end date (since remember, you're on Cat Time so the amount of activities you do depends on your cats). The winner is the cat with the most points by the end!
Examples of tasks (there would be at least 20):