Final answer:
In the story, the child and Zaroff both go to great lengths to amuse themselves.
Step-by-step explanation:
The trait that the child and Zaroff share in the story is that they both go to great lengths to amuse themselves. In the story, the child is seen playing imaginary games and putting on elaborate displays of aggression and defense. Similarly, Zaroff hunts humans for his own amusement and creates a dangerous game on Ship-Trap Island. Both characters engage in activities solely for their own entertainment and enjoyment.