Interesting question. Well, you aren't going to find any "magic" in this excellent short story of the "Harry Potter," swish-and-flick, "Abracadabra!" variety. If you consider that there is magic in this tale of horror it lies in the supernatural way that the eye of the old man comes to haunt the unreliable and mad narrator and then the way that the old man's dismembered heart magically seems to continue beating, in spite of having been hacked out of the man and buried.
Consider what the narrator says about the eye:
I think it was his eye! yes, it was this! He had the eye of a vulture - a pale blue eye, with a film over it. Whenever it fell upon me, my blood ran cold; and so by degrees - very gradually - I made up my mind to take the life of the old man, and thus rid myself of the eye forever.
It is clear that the eye assumes supernatural importance in the way it dominates and oppresses the narrator. When he finally goes into the old man's room at night to kill him, when he lets light on to him, he sees only the eye, which "chilled the very marrow" of the narrator's bones.
Secondly, the way that the heart continues beating and haunts the murderer with his crime could be described as "magic." As the narrator speaks to police and tries to assure them that there is nothing wrong, he hears a sound that increases in intensity:
It was a low, dull, quick sound - much such a sound as a watch makes when enveloped in cotton.
This sound of the man's still beating heart gradually becomes louder and louder, and its effect on the narrator is to literally drive him insane until he is forced to confess his guilt and reveal the corpse.