I can understand someone who isn't familiar with what's going on thinking that this is just a bunch of dogs being released on a boar, and I can see how that would upset some people who don't know what they're looking at. The reality of the situation is that this is one of the most humane ways to hunt wild boar because it systematically minimizes the chance of long-term suffering.
The first set of dogs are used for baying, and that just involves finding the boar and keeping it more or less in one place. You'll notice that none of them actually engage the boar and mostly just run away when it charges. These are typically fast, medium-sized dogs, and you'll notice that they aren't wearing any type of protection (though I think one of them is wearing a tracking collar, which is normal).
The second set of dogs are used for catching, and that involves physically subduing the boar once it's been bayed. You'll notice they're wearing throat and neck protection. This typically involves grabbing the boar by the neck and dragging it to the ground and keeping it immobile. I want to point out that the boar isn't really being hurt as much as you might think in this step of the process because of how ridiculously tough they are. Catch dogs are typically large, slower dogs wearing various types of protection.
Once the boar is immobile and secured, you can go in and either hog tie it if you want to relocate it, or you can kill it at close range with no chance of unnecessary suffering.
As far as "we have guns and can kill an animal in a second," it doesn't work like that in the real world. The best way to virtually guarantee that this boar is going to suffer unnecessarily over the long term is to shoot it before it's subdued and immobile.
