For most of the story, the point of view is in the third person. The last part of the story, however, is told from something of a first person point of view.
At first, the narrator is just a limited third person observer. He is just saying what is going on. In the second section of the story, the narrator is still third person, but is not so limited. The narrator knows some of Farquhar's perceptions and thoughts.
Finally, in the part after Farquhar supposedly falls into the river, the story is told from his point of view. It's not exactly first person because the narrator does not say "I," but it is clearly from someone who knows all about what Farquhar is thinking. So you could, I suppose, call it an omniscient third person narrator, though eNotes's summary calls it "modified first person."
In paragraph 5 the point of view shifts when Farquhar closes his eyes, thereby shutting off the outside world of his perceptions and opening up the inner world of his imagination. Our attention is thus directed toward those things that he thinks he sees and experiences. First we learn of the apparent slowing of his watch, followed by his dream or belief that he is actually escaping. (He has this extended perception once he is actually being hanged.) In paragraph thirty-seven the point of view becomes abruptly and cruelly dramatic. There is no more probing into Farquhar’s mind because he is dead.