People confuse killing for fun as a phenomenon known as "surplus killing".
Surplus killing doesn't happen often in nature due to the predatory defences prey use that mitigate surplus killing (i.e fleeing, fighting and more fleeing). For example, a fox going into a chicken coup will count as surplus killing, where it will attempt to kill and stash multiple cornered and mostly defenceless domesticated prey. Sometimes they can't eat all of the prey killed, often because there are too much or they've gotten full, stashing for later. Ironically quite mirrors in game KOSing situations, where there are multiple prey items all without any caution laying about in Oasis. Again all predators are capable of surplus killing it's just that when one animal dies, the rest flee for safety, often only killing one prey per hunting trip. Additionally, there is risk in getting greedy, your hard earned kill may end up getting stolen if you continue to chase, you might end up with a kill but no meal :(
Alternatively, the animals that are described to hunt for fun are mostly instead related to behavioural and hormonal factors. Orcas or Killer Whales are one such, observed launching seals and other unfortunate animals caught in their grasp. It is likely that it is immature or hormonal Orcas that are "playing" (play is actually very important for survival, developing the hunting skills needed in adulthood) with their prey. With multiple methods of prey dispatch, Orcas adopt several methods of hunting that differ between pods. Launching seals to the stratosphere helps reduce risk of the seal biting back. Animals that play do somewhat associate with "fun" but in the wild this is important for survival. What is once observed as play is now methods of competition between species (i.e male lions wrestle as young, building strength and skills to wrestle with adult males to survive). Lastly, playfulness links with intelligence with animals who are more intelligent are more active and playful as young and that activeness helps build the knowledge, bonds and generational skills to survive such as Orcas hunting or Elephants forming migratory paths.
To summarise as much as I can, animals don't kill for fun or sport, they kill to eat. Behaviours observed as killing for fun are instead examples of opportunistic surplus killing, which takes several factors outside of the hunt and play which animals often don't do for fun in the wild but rather to build/teach the skills needed to survive when young and to form bonds between family. Sorry for the wall of text but these things are incredibly complicated and misinformation easily spreads.
