I have a weird sort of in on this, in that my grandparents are exactly the kind of people who love The Road to Mandalay. I think the clever thing about reciting a poem like that is it appeals to a broad spectrum of conservative voters: the low-end, who will enjoy the thumb in the eye of 'political correctness', the mid-level, who feel like the british empire was good, then the 'intellectuals' (like my grandparents), who are very fond of poetry and Kipling, and like to think of themselves as more intelligent and refined than their proletariat opposition.
The nice thing about it, is it's a spectrum. If you're in the conservative-intellectual bracket, you still probably enjoy the provocation of the politically correct, and the imperial nostalgia stuff. If you're in the conservative-middle-brow bracket, you still feel good about the fact that your racism is being associated with Great British poetry.
I don't think he's a genius, or that he's playing fifth-dimensional chess, or something. I think it's just an advantage of this whole bumbling persona - that he can go to events like this and basically do what he wants. So when he thinks up some kind of stunt - like reciting a colonialist poem, or getting stuck on a rope, or whatever - he can go ahead with it, because it fits with his image. That gives him a whole range of communicative strategies most politicians don't have. What he actually communicates (the blend of dogwhistle racism and attention-seeking) is actually pretty normal.