Typically the phrase "may he rest in peace" is spoken by a priest. A priest would utter those words to a dying man after he confesses his sins. When a priest says those words, he is essentially telling the dying man that his sins are forgiven and that he can now die (rest) in peace.
Montresor is not a priest, but his utterance of those words shows him taking on the role of a priest. Montresor started the entire story by telling his audience how Fortunato had hurt him (sinned against him) thousands of times.
"THE thousand injuries of Fortunato I had borne as I best could;"
Fortunato had done so many injuries and insults to Montresor that Montresor vowed revenge. Fortunato then pulled off the perfect revenge. Fifty years later and still nobody knows what happened to Fortunato. Montresor saw his goal to the end, and cleansed his spirit of those angry feelings. Because Montresor eliminated Fortunato, Montresor no longer holds any grievances against Fortunato. In essence, because Fortunato is dead, Montresor has forgiven him. By uttering "in pace requiescat," Montresor is saying that he forgives Fortunato's thousands of injuries and wants him to finally rest in peace.