It is clear that the main way in which the author uses the sense in this story is to evoke the absolute horror and fear of the situation of Tom Benecke as he goes out onto the ledge of his apartment and faces death. Consider the following passage:

In the fractional moment before horror paralysed him, as he stared between his legs at that terrible length of street far beneath him, a fragment of his mind raised his body in a spadmodic jerk to an upright position again, but so violently that his head scraped hard against the wall, bouncing off it, and his body swayed outward to the knife-edge of balance, and he very nearly plunged backward and fell. Then he was leaning far into the corner again, squeezing and pushing into it, not only his face but his chest and stomach, his back arching; and his fingertips clung with all the pressure of his pulling arms to the shoulder-high half-inch indentation in the bricks.

Good authors try to make the story real to us by painting a picture of the action by appealing to as many of our senses as possible: sight, taste, smell, touch and hearing. Note here how this terrifying passage clearly conveys great sight and touch senses - we can imagine the horror of Tom as he looks down, and we can feel the pressure of the corner of the building pressing into Tom's body as he clutches it for dear life. It is this use of senses that makes this such an effective tale, because we are able to imagine the absolute terror of a man so high up clinging to the outside of his apartment building, with death but an inch away. Not a good story for those that suffer from vertigo!