I don't really expect vegans to understand hunting or why so many people enjoy it, but I'll give this my best shot.

First, obviously, is food. Most hunters have a deep conviction about taking responsibility for the meat that they eat by hunting for it themselves. Depending on how well things go, a hunter can get enough meat to feed himself or his family for a good chunk of the year. A lot of hunters also generously donate some of their meat to charities that provide meals for the hungry -- millions of meals every year, all thanks to hunters.

Hunters care about the environment, as well, and contribute millions to conservation efforts that improve wildlife habitats, fund conservation research, preserve land, maintain and manage parks/refuges, and so much more. Hunting is also an important factor in keeping certain wildlife populations balanced and sustainable (deer in particular). All of this is beneficial not only for the species that are commonly hunted, but also for other ecologically important species that dwell in those same refuges. Hunters are the driving force behind organizations like Ducks Unlimited, which manages, restores, and preserves wetland habitat for waterfowl, in addition to other conservation projects.

Finally, hunters just enjoy hunting, and not in a psychopathic, sadistic way. Hunting provides a unique connection with the primal aspects of our humanity that most of us have completely forgotten. That, I think, is what you're seeing in this video. My guess is that these are first time hunters, so getting that first kill is an emotional moment. Especially for those kids who, being raised in hunting families, know the value of putting food on their family dinner table. It's a sense of accomplishment. That girl with the bow, for instance, probably spent forever practicing to land that shot.

Hunting is an activity that requires a lot of skill and knowledge about their tools, their prey, their environment, and how each of those interact. Hunting is engaging with the environment by actually participating in it, involving yourself in the cycle of life and death that we all take part in one way or another and learning to respect it. This is how they choose to be part of that, and that's the difference between hunting for your food vs. picking it up at the store: the hunter, at least, takes that life and death responsibility into his own hands and accepts it for the unavoidable reality that it is.

This doesn't apply to poaching or trophy hunting, which is selfish and unacceptable, in my opinion, but it does represent the majority of hunters with whom I am acquainted.