Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Sardonic
Any narrator who describes a condemned man as "engaged in being hanged" (1.4) automatically qualifies for the Sardonic Tone Award (the Tone-y Awards ceremony is only slightly less boring than the Oscars). Sardonic basically means bitter or cynical, and boy is our narrator both of these things.
The narrator describes the execution with precision, but also with his tongue in his cheek. Check out how he describes Farquhar's commitment to the southern cause:
No service was too humble for him to perform in the aid of the South, no adventure too perilous for him to undertake if consistent with the character of a civilian who was at heart a soldier, and who in good faith and without too much qualification assented to at least a part of the frankly villainous dictum that all is fair in love and war. (2.1)
The narrator calls the famous saying – "all is fair in love and war" – "villainous," but refrains from calling his protagonist "villainous." Basically, he aligns Farquhar with a villainous creed, but leaves it up to us to decide about Farquhar's action. This is fitting, since this is a story focused on perception and interpretation.
Although sardonic might not be the nicest word to describe someone, it actually works incredibly well for the story. Because the narrator remains sardonically detached, he is able to describe Farquhar's fantastical escape as though it is actually happening.