Looking at the descriptions of the different plot types I'd have to classify this one as mostly comedy. Comedy is defined as a sympathetic central character overcoming difficulties to come out better in the end. Mary Cunningham is painted very sympathetically -- here she is the poor widow with young children trying to do her best to survive at something she is obviously unsuited for -- a position that has been thrust upon her by her husband's untimely death. Along come our heroes, who slay the dragon (Sloan) and get Mary the money she needs to start a new life back East -- a life she longs for and is better suited to.
Yes there is some overcoming the monster (Sloan/Plummer) and there are always quests -- but these are fairly minor ones here. As Calico notes this could be considered a slow action, lightly plotted story -- but really I think this one is in the nature of an Arthurian tale of "right makes might" and the knights errant slaying the dragon to rescue the damsel in distress. This was a good choice for an early episode in the show to set up our boys as do-gooders despite their outlaw natures. In this tale they are acting contrary to their own interests in order to help Mary, yet the actions they take and the ways they solve their dilemma reek strongly of the outlaws they are (threat of violence to Gorman and extortion with Sloan, plus breaking and entering at Sloan's house). The central plot, however, revolves around Mary's situation. Therefore, I'd classify it as a comedy.