Well, remember that the narrator in this great short story concerning death and an incredible escape is not an actual character in the story, so we are not able to treat him like a character and have any definite idea about him. However if I understand your question correctly, you seem to want some kind of comment on the narrative style. What is interesting about the point of view in this story is that it alternates throughout the story to reflect the altered state of Farquhar in his frenzied escape from reality. Note the following example:
"To be hanged and drowned," he thought, "that is not so bad; but I do not wish to be shot. No; I will not be shot; that is not fair."
He was not conscious of an effort, but a sharp pain his wrist apprised him that he was trying to free his hands. He gave the struggle his attention, as an idler might observe the feat of a juggler, without interest in the outcome. what a splendid effort!--what magnificent, what superhuman strength! Ah, that was a fine endeavour! Bravo!
Note how Bierce alternates between a first-person and a third-person-limited perspective here. This is a technique that conveys Farquhar's dream-like disassociation with his own body and reality at large.
So, if you are thinking of the narrator, it is better to consider how the point of view is manipulated by the author, and what effect is achieved by doing this.