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.
I do like your idea but that doesn’t mean I didn’t like Stray. I finished the entire game and I loved it. The cat was adorable, the friends I made a long the way were interesting and I really felt for them despite their, uh, limitations. Just leaving it at that to avoid spoilers as I only saw that it was a cute cat game before I tried it and enjoyed being surprised by how it ended up.
But yes, I do think a game like you’re describing would also be fun. Maybe not as a stray cat, per se, but maybe as a small breed of wild cat living away from humans so you don’t have too much interaction with them and they’re something you’re inherently distrustful of.