You are right in identifying that this essay includes rather a gruesome and, arguably, unnecessary description of how the poor elephant that Orwell did not actually want to kill met his end at Orwell's hand. Note the following rather graphic description:
I fired a third time. That was the shot that did for him. You could see the agony of it jolt his whole body and knock the last remnant of strength from his legs. But in falling he seemed for a moment to rise, for as his hind legs collapsed beneath him he seemed to tower upward like a huge rock toppling, his trunk reaching skyward like a tree. He trumpeted, for the first and only time. And then down he came, his belly toward me, with a crash that seemed to shake the ground even where I lay.
We definitely feel sympathy for the element, but also, let us remember the real reason for such a protracted description: it helps us feel greater sympathy to for Orwell in the impossible position in which he finds himself. For Orwell himself says he was not a good shot nor a good hunter, and he did not want to kill this animal that he was expected to slaughter for a public display in front of the Burmese that despise him so.
The main purpose for shooting the elephant, which was really unnecessary for him in the circumstances, but it was important to do so as the elephant had make a rampant charge and assault on the village crazily, in its wake destroyed a truck, a hut and a solo villager. The villagers were rather upset and frightened about the ordeal and the scene they are witnessing, so it was best to kill the elephant so that the madness and the lunacy would not be carried on further and peace would be restored. The narrator also did not want to look vulnerable in front of the villagers in case of rebellion, he displays a power of authority and control over them, to show his solidarity and obtain order in the village, without trowing the village into a dark mess of bloodshed.
His vivid description of the death of the elephant was to show his conflict of emotions in his soul, the ethical and moral agonies he had suffered throughout the trouble at hand. He was helpless and the clash of emotions make him yelping in despair and he has guilty conscious for killing a life.
In my opinion, he did the right choice in the right time as at time, the Burmese government didn't have really good weapons technology and the poor villagers had no apparent defenses or attacks against these mighty beast of Africa. They would be dumb and stupid if the villagers allow the elephant to roam around freely and cause mass destruction, or even complete mayhem. Next, the destruction of the village would cause lost in property and money as the elephant had destroyed a house, killed a bull and raid a stall even. There would be huge amounts of money needed to cope with this financial loss and the time to rebuild this ruins would be painstakingly long and tiring. People would have to find another shelter to live in or live in the horrid cold weather. People would die of starvation or freeze to death.
George Ewell add vivid description to the dying process of the creature is to justify the killing of the elephant to be right choice and the purpose of not getting straight to the point is to show the payback that the villagers give to the elephant for completely killing away human lives and killing all of their livestock and their life produce they feed on. They wanted to prove a point that the elephant death is a superb choice and the exaggerated death of the elephant is cleverly described by the narrator
You can see this story as an allegory to the colonial oppression practiced in places like Burma. While the Elephant is no longer a danger to the people, it still must be shot because that is what the people expect, and if he does not shoot the elephant they will laugh and ridicule him.
The long description only serves to further the sense of waste and hopelessness. Shooting the elephant was a terrible thing, as was colonial oppression, and the sight of the elephant dying is sure to leave a mark on the reader and drive home the point.