Arguably, Orwell chose to only include his own voice because he wanted to really highlight his point about the evil of imperialism. Specifically, that imperialism forces everybody, including the imperialist, to act in a certain way. Had Orwell included the voices of others, like the Burmese spectators, for example, there is a chance that the story would shift its area of focus and, therefore, detract from Orwell's central argument about imperialism.
The absence of additional dialogues is, therefore, a major strength of Orwell's story. Remember that this story isn't really a story about shooting an elephant. As Orwell himself admits, this incident is important because it taught him something about the nature of imperialism and that is why he chooses to relate it.
So the shooting of the elephant is, in fact, a metaphor for the evils of imperialism. Imperialism destroys the identities of imperialists and natives alike, just as Orwell had to literally destroy the elephant as part of his duties.
What we find, then, is that by only including his own dialogue, Orwell forces the reader to absorb his message without interference from other sources.