Your "X don't Y per se, they Z" macro take reveals misunderstanding. In the original, Y and Z are different actions with different intent (use human as ball dispenser vs try to make the a human happy like a dog would) whereas you just make your Z to be a technical definition of Y.
No matter how many times I read it, I interpret his Z as little more than a technical definition of Y. In both, Y and Z are the same actions.
Because we fundamentally disagree on the intent. I don't agree that a cat is engaging in parasitic exploitation of the human toy-thrower, and I don't agree that a dog is toiling in servitude to the thankless human who keeps throwing away the retrieved item. They both love chasing things, they both understand that to chase the thing again they need to return it to the human, and they both appreciate the positive reinforcement, bonding, petting, and attention when they do so.
It's just logic. A cat has infinite ways of exercising on its own and actually most cats do just that, so it's pareto principle to think about "playing fetch" as simply convenient way of exercising a chase something that incidentally involves a human throwing things rather than birds or mouse.
A dog however simply does not do things on its own much, dogs are maybe even more social than humans and live in packs (dog owner is de facto pack leader). Play is more social for them. Take out peer/leader to play with and half the excitement is gone. Dogs generally would not consider mechanical ball dispenser equally exciting of a partner