The quote you have identified is narrated to us by the distinctly unreliable narrator who tells us the tale from his profoundly distorted point of view. Having stolen into the old man's room with the specific intention of killing him, and knowing that the old man is aware of the presence of some villain and is terrified as a result, the narrator opens his lantern to reveal a narrow beam of light which fell upon the "vulture eye" of the old man that the narrator is so obsessed by.
What is important to note about the quote you have identified is the response of the narrator to seeing the eye wide open. He grew "furious" as he looked upon it, as it strikes him with fear and loathing and the sight, we are told, "chilled the very marrow in my bones." The focus on the eye alone emphasises the impact that it has on the narrator and the curious fascination that it is able to exert over him.