Mark Twain can be classified as a literary comedian because his writings do much of what modern day comedians do now -- point out social ills in a light-hearted tone.
Twain may appear to write simple adventure narratives, and on a surface read, novels like Huck Finn are exactly that, a story of a boy on an adventurous river float. However, upon deeper examination, Twain uses "silly" scenes or events to point out real world problems or social constructs. Huck's narration and response to the duke and king are a good example of Twain's sarcasm, satire, wit, and irony.
Many modern day comics are very similar to Twain in that regard. John Stewart and Tina Fey are two examples that come to mind immediately. They love to point out social injustices and oddities with a humorous delivery. Funny, but no less poignant. The weekend update on Saturday Night Live is a lot like Twain or any opening monologue done by Leno, Letterman, and Fallon.