Come on, this is not offensive to anyone except those who don't get it. So he uses the n-word which many dislike.
AFRICAN, n. A nigger that votes our way.
All he's saying here is that if they're working with 'us', we'll treat them with a passible amount of respect (African), whereas if they don't, we insult (nigger). He uses the word again in:
MINSTREL, adj. Formerly a poet, singer or musician; now a nigger with a color less than skin deep and a humor more than flesh and blood can bear.
Ever seen any films of The Black and White Minstrel Show? Well, it's a load of white Welsh singers (for their voices) who are wearing a cross between war paint and sun block. Here the term nigger is used as an insult - to the people who have little talent and less entertainment value.

These are the only two times the word 'nigger' is used in the entire Devil's Dictionary..

MULATTO, n. A child of two races, ashamed of both.
Maybe this isn't so much the child who is ashamed, but both races. The child is neither fully white, and a part of everyday white, civilised society, nor fully black and part of the closely knit community who have traditionally been very closed. Add to this the fact that a white person and a black person err... did something together... and it is a reminder that the difference is very, very, very little.
NEGRO, n. The piece de resistance in the American political problem. Representing him by the letter n, the Republicans begin to build their equation thus: "Let n = the white man." This, however, appears to give an unsatisfactory solution.
This isn't too funny, to me. But it makes a valid point. Those working out their equations start with the premise that everyone is equal (n = the white man) but then automatically ignore everyone who is not white (it is the start of every proof, where n is the set to consider).

It should be remembered that this man is sitting on the fence, poking holes in the side of everybody. He attacks Christianity in the guise of being a Christian bigot, he attacks those who write dictionaries as he writes his own. No one has been set out for special treatment, whether left out or attacked, except those who are bigots, hypocrites and have other intolerable vices.

They're not even his views, for Christ's sake!