Just an open world survival game, only you’re a cat, dealing with regular cat problems. You have to hunt, avoid larger animals, compete with other cats, figure out which humans are dangerous and which will give you treats, judiciously spray things to maintain your territory, maybe mate and reproduce (your sex and fertility status are basically difficulty settings), etc.
You start out as a housecat going on a spring vacation with your family, and that’s the tutorial section. Then your humans accidentally leave you behind at their country vacation home, and then the difficulty is just the passing of seasons. See if you can survive winter and see your humans again next spring.
Make it people would love it, though I’d say the opening ends with the place being on fire so as the cat needs to escape and that’s where the separation stems from, because I couldn’t imagine just forgetting my cat.
That just made me think you could also make the game where the family abandons the cat and it hunts them down and kills them, same premise though, in the end the cat finds the family.