We could argue semantics all day. A father and son sport hunting together could be referred to as pack bonding.
There are well documented reports of ranchers in the western US finding cattle that have been killed by wolves and not consumed, in fact sometimes several cattle are found in the same location and none show signs of consumption by the wolves.
And anyone who has owned a cat will tell you stories of the pet killing mice or birds for "sport." Many will say, it's their natural instinct...well, we are just animals too.
But the semantics are important here.
Some members are alluding to the fact that trophy hunters are somehow displaying something that is innate through evolution. Members are then trying to support that by humanizing animal behaviours.
Hunters kill. That much is the same in nature. But Trophy Hunters do so to be able to say/show/know that they killed that particular animal. If it was for the food they would eat it. If it was for the sake of seeing it in the wild they could take a photo and go home. The culmination is the pull of that trigger and often, the photo-op over the corpse. The animal's death signals the success of the outing.
For regular hunters, despite elation at the time of the kill, the meal on the plate is the ultimate sign of the hunt's success because that was the hunt's original purpose. Some may hunt to protect their crops/cattle. If it did not threaten their crops/cattle, they would not hunt that animal. They are not killing for the sake of killing.
Aside from the motivations I listed earlier, the examples you gave could be attributed to a behavioural positive feedback loop after a particularly intense hunt in the case of the wolves (akin to feeding frenzies in sharks for example), or a cat using its hunting skills out of instinct because all its dietary needs come from a tin. The movement of the bird hopping or the mouse scurrying flips that switch. It is a hardwired reaction: it is not recreation in the human sense.
In the animal kindgom, there are certain major motivators. The instinct to survive, to feed and to procreate and all of them are there to serve to progression of genes to the next generation, in one way or another.
One thing that does set humans is that we can control evolutionary instincts in behaviour. That is why we have a system of ethical values.
For me, ethics are the crux of this issue. Differing ethical values about what different people perceive as acceptable and responsible.
You don't kill an enemy; you bankrupt him or beat him in the election primaries. Or maybe steal his girlfriend.
That is not a predatory instinct. That is a "desire to mate" instinct.
Get the Alpha Male status and you get the girls. This has nothing to do with killing.
Male-on-Male bouts in the wild only last until one of the contenders backs down. That is rarely when one dies although it can come to that if both feel they are strongest. Often, some vocalisation and posturing is enough to show the under-dog he is no match for the "dude" opposite. It ends there, with no loss of blood/life.
The macho mentality is just that: the big car, the big wrist-watch, the showy behaviour, even the friday night bar brawl. There is a reason these are often the butt of the "compensation" joke. This has nothing to do with the acquisition of food, which is what predation is designed for.