This story can be considered humorous in that there is a lot of irony contained within the text. Scoresby is a fellow who gets by basically on luck... dumb luck, to be completely frank. He cannot pass anything in school, so the reverend, a man of strict veracity (amusingly enough), decides to help the poor boy fail with some dignity by drilling him on Caesar... the only topic he really knows anything about. It turns out the only questions asked on his exam were about Caesar, thus enabling Scoresby to earn high marks on the exam.
Another example that comes to mind is the battle in the Cremean War, during which Scoresby misunderstands an order, mistakes his left from his right, and surprises the Russian reserves, causing everyone else to believe he is a military genius. This clearly isn't the case, but one has to wonder... at a certain point, doesn't consistent luck perhaps lead to skill? One can't be lucky each time, although it seems Scoresby is. Maybe he's not as stupid as the reverend thinks?
The conversational style in which the reverend tells the story (to the narrator, as a follow-up to the conversation during which he tells him that "privately, he's an absolute fool") also lends to the humor.