It's hard to tell if there is a clear distinction between social/"fun" and food rewards.
Experiments have shown an "anti-freeloading" effect in most species, except cats: Within reason, a reward for work is preferable over the same reward for no work.
I also don't think cats care specifically whether or not their fun and playing leads to food or not. It just happens that their idea of fun would lead to discovering and killing small animals in a natural setting. Maybe they hunt because it's fun, not just because they are hungry.
The neighbour cat spends ages in my garden in hunting postures staring at insects and occasionally chasing them. Then she'll lie down and enjoy the weather for a bit,continue her patrol and come back a couple of hours later and repeat.
And when I was a kid we had a cat that we eventually discovered liked sitting in the berry bushes in the garden and kill birds. We discovered it because she didn't eat them, but just left them there and we eventually found a whole pile.
She did on occasion hunt for food too, but mostly when the prey was out of the norm, like once when she caught a large rat - only the tail was left. Of course I don't know how much she ate out at night, though.
> Maybe they hunt because it's fun, not just because they are hungry.
My well-fed cat spends most of her time indoors but is allowed out. She doesn’t bring back creatures very often, but a few months back, at the start of summer, one night she killed and brought back (through an open window) three rodents in one night. Each time, she left them in the hallway, came up to the bedroom and meowed until I woke up. Then she lead me to the kill, made absolutely sure I saw it and then left it there, seemingly losing interest. She did it three times that night until I finally just closed the window.
This is a well fed cat and she didn’t attempt to eat her kills; she did not do it for food.
In my experience with cats, they also like to hunt flies, bottle caps, feet, their own tails, leaves blowing in the wind... etc. I think they’re just hard wired to enjoy hunting “things”.
There's a theory that when cats do this they're bringing you food - either to say thank you for feeding them, or because they think you're a big dumb hairless cat who hasn't worked out how to hunt.
It's impossible to know for sure without asking the cat, and the cat isn't telling.
Cats do enjoy chasing and pawing at things - or at least, they're hardwired to chase and paw at things, which is not quite the same. At the very least it seems to scratch an emotional itch for a while.
It's understood in Africa that if you're stalked by a lion, you should either face it and run towards it, or make loud noises to try to scare it away, or maybe both - because if you try to run away, its stalking instinct is triggered and you'll be on the menu.
Cats are complicated, and learning how to communicate with a cat is like learning a non-verbal language. It took us a long time to stop misinterpreting our cat, and it took our cat a while to work out how to communicate more clearly. It's still a work in progress, and surprises continue to happen.
Experiments have shown an "anti-freeloading" effect in most species, except cats: Within reason, a reward for work is preferable over the same reward for no work.
I also don't think cats care specifically whether or not their fun and playing leads to food or not. It just happens that their idea of fun would lead to discovering and killing small animals in a natural setting. Maybe they hunt because it's fun, not just because they are hungry.