It is highly ironic that Orwell in this essay explains how he was forced to do something that he did not want to do or see any need for doing because of the mob power of the Burmese and the pressure of the "sea of yellow faces" that expect Orwell to perform "a magic trick" in killing the elephant. This of course points towards the way that the power relations are completely reversed, and supports Orwell's main thesis in this excellent essay, which is that "when the white man turns tyrant it is his own freedom that he destroys." We see, in the quote that you have highlighted, Orwell being forced to act through nothing more noble than the fear of being laughed at. Note the following quote as well:
The sole thought in my mind was that if anything went wrong those two thousand Burmans would see me pursued, caught, trampled on, and reduced to a grinning corpse like that Indian up the hill. And if that happpened it was quite probably that some of them would laught. That would never do.
Note the way that this situation reverses the expected patterns of power. Orwell, as a colonial officier, in theory should have power, and yet this quote reveals his fear of being laughed at, which actually gives the Burmese incredible power and renders Orwell powerless. Orwell recognises the immense irony of this and how it limits his own freedom and turns the Burmese people into a kind of tyrant as they have expectations that they want to be met.