There is a third option: he isn't making a point, nor does he casually use the word himself, but that the characters use the word and Twain is being authentic to what he feels his characters would have said.

For what it's worth, Wikipedia notes that

Nineteenth-century English (language) literature features usages of nigger without racist connotation, e.g. the Joseph Conrad novella The Nigger of the 'Narcissus' (1897). Moreover, Charles Dickens and Mark Twain created characters who used the word as contemporary usage. Twain, in the autobiographic book Life on the Mississippi (1883), used the term within quotes, indicating reported usage, but used the term "negro" when speaking in his own narrative persona.

My admittedly limited understanding is that "nigger" started out as a variant on "negro" as a generic word for a black person, and gradually gained its racist overtones by the time of the First World War. So even if Mark Twain was using the word in the 1870s, he didn't necessarily mean it as a slur - it was just a slightly old-fashioned, country word for the modern, scientific "negro" (as it would have been seen at the time).