The fact that Rainsford rests easily in the bed of the man whom he has just killed indicates his transformation from a man with ethics to one who does not have qualms about killing another human being. Indeed, there is a significant character change indicated by the last ironic line.
(See the question on irony, as well.)
The last line is important because it indicates the story's eventual outcome. The line states that Rainsford slept with immense pleasure in Zaroff's bed. This tells the reader that Rainsford has killed Zaroff and is the ultimate winner of the "contest". Zarof becomes a victim of his own game because he underestimates Rainsford. "The prey has killed the predator."