Why is the limited third-person point of view appropriate for this story? Point of view refers to the vantage point from which the story is told.
In my opinion, this is because either of the other kinds of point of view would completely ruin the story.
This story is made interesting in large part by the surprise ending. In the story, part of what is interesting is wondering what is going to happen to Farquhar after he has been hung. He has fallen into the water. Will he escape?
If the third person narrator had been omniscient, he would have known that Farquhar was dead and that this whole thing was just in his mind. Not much fun there.
If the story were told from Farguhar's point of view, it would have to end with "and then I died," which is sort of hard to believe. That's why the author has to switch back to the third person before revealing that Farquhar is dead.
So the limited narrator makes the most sense to me because the suspense can be maintained.