The text plays on the expectation of the word 'me' to refer to the speaker's perspective, but in the context of egotism, it humorously suggests that the egotist should be interested in the speaker, which is an unexpected twist. It does not rely on different meanings of a single word or similar sounding words, but rather on the subversion of the listener's expectation.
An egotist is a person who is more interested in himself than in me .