This is the sport I like best - mouse tossing, shown in a good photo of the late Toby. The mouse is dead, but Toby is playing with it, tossing it into the air and then pouncing on it.
Why it's such fun is that it is part of our hunting repertoire, hard wired into us so that we carnivores can survive. Hunting isn't just what we do: it's what we are. And this kind of playing is part of it.
Some of us claim that playing with prey before killing it is "dazing" it, ie tiring it out so that if we make a mistake with the kill bite and don't finish it off, it will be too tired to bite us back. Or that, in the case of unusual prey like rats or snakes, it allows us to assess how to deliver that final bite. Other cats say that only well-fed cats waste time with this sort of thing: wild and feral cats just get on with the important business of killing and eating their next meal.
My uncle George used to hunt live mice and rabbits, but my more scholastic life has meant that I don't have a good hunting field. So I have to put up with small artificial mice, little bits of scrunched paper, or small stuff like a bit of dried pasta or a bean that can be shunted round the kitchen floor.
The point of this play is that the mouse/bean must move. Static prey doesn't do it for us. So we poke and toss to get that movement which sets off our hunting reactions.
Whether it's a real mouse or just a substitute for one, there is nothing cats like better than playing in this way. Purrlease, humans, don't just give us the toys: throw them for us.