Rudyard Kipling's style in "The Man Who Would Be King" echoes the famous method of telling a story from someone else's perspective and "reporting" on it as an objective listener. In his era, it was common for travelers to relate tales told to them by others, which allowed the more fantastic stories to have a level of separation between the re-teller and the original story. Kipling's short story predates a more famous example of this style, Joseph Conrad's Heart of Darkness, and they share several attributes.
Kipling writes the sordid tale first from the perspective of an impartial observer -- the narrator -- and then inside that telling from the perspective of the man who experienced it firsthand -- Carnehan. He is able to avoid justifications and excuses, since all we read are the words of Carnehan, and we don't see his inner thoughts. For his part, the narrator is appalled by the tale and horrified by the implications:
He fumbled in the mass of rags round his bent waist; brought out a black horsehair bag embroidered with silver thread; and shook therefrom on to my table—the dried, withered head of Daniel Dravot!
I shuddered, for, in spite of defacements manifold, I recognized the head of the man of Marwar Junction. Carnehan rose to go. I attempted to stop him. He was not fit to walk abroad.
(Kipling, "The Man Who Would Be King," gutenberg.org)
He also presents the sympathetic ear of the listener and allows the reader to avoid full condemnation of Carnehan and Dravot's schemes. This extra layer of objectivity strengthens the story by adding the illusion of honest reporting; we have no reason to distrust the narrator, but we have significant reason to distrust Carnehan, who predicated his downfall with lies. However, we can believe that the narrator faithfully related the story as he heard it; other interpretations are left up to the reader.