Both stories have characters that try to overcome the seemingly impossible task in front of them. They are also both warned about the perils in front of them. In The Most Dangerous Game, the captain warns about the floating lights, but they press through. In To Build a Fire, the old man warns about the oncoming cold,and that he shouldn't keep traveling on, but he persists.
Both characters also have to persevere against nature. In The Most Dangerous Game, the hunter has to avoid quicksand, and in To Build a Fire, he has to avoid the water springs.
There are also dogs in both stories. In one story, they are the main character's friend, and in the other, they are his enemy.
Those are just a few of the similarities and differences in The Most Dangerous Game and To Build a Fire.