What myth of Southern life does Twain satirize in the Sherburn/Boggs incident?
I think that what Twain is satirizing here is the Southern obsession with honor that could be seen in that region in the time before the Civil War. In the value system of the South, men of "good" families and backgrounds ("gentlemen") had to defend their honor whenever they were insulted. This led to such things as duels, which were quite often fought.
In this chapter, Colonel Sherburne is defending his honor. It is not acceptable to him to let a drunkard say bad things about him and make him look silly. Because he needs to protect his honor, he shoots Boggs.