Absolutely true. Canids and felids in particular hunt more for sport than for food. Wolves have been observed having all sorts of fun killing an entire flock of sheep. Foxes hunt and kill mice and birds without eating 'em. And I used to have a cat who did nothing but hunt gophers all day long; within 3 years he'd completely exterminated them in my neighborhood.
Incidentally my neighbor runs a twice-weekly foxhunt, tho the usual quarry is coyotes (mostly chasing, they usually don't shoot 'em). The local coyotes have gotten so into being chased by dogs that they come down to the kennel the night before a hunt and get the dogs all riled up and ready to go.