Well done for spotting this detail. Of course, the inclusion of this first story, cited in Chapter Four of this tremendous novel, is no accident, and it presents an ironic commentary on the plot. Note what the subject of this first short story is:
It was a dark little tale about a man who found a magic cup and learned that if he wept into the cup, his tears turned into pearls. But even though he had always been poor, he was a happy man and rarely shed a tear. So he found ways to make himself sad so that his tears could make him rich. As the pearls piled up, so did his greed grow. The story ended iwth the man sitting on a mountain of pearls, knife in hand, weeping helplessly into the cup with his beloved wife's slain body in his arms.
Note the parallels between this story and Amir's situation. Both the man of the story and Amir sacrifice the person that is dear to them for their own motive. For Amir, however, he has no magic cup. He sacrifices Hassan for his own safety and out of a sense of his own cowardice. He, however, like the man, is literally grief-stricken and haunted by the sacrifice that he has made, and it takes the rest of the novel for Amir to deal with what he did when he was a child. Thus the first story serves as an ironic foreshadowing of what is to come and of the own sacrifice that Amir makes by letting Hassan be raped while he watches and does nothing to preserve his own safety.