After spending the night in a tree, General Zaroff manages to track Rainsford's path through the forest and approaches the tree that Rainsford is hiding in. However, the general does not look up at Rainsford and smiles before he walks away. Once the general has walked a considerable distance, Rainsford climbs down from the tree and creates a trap known as a Malay mancatcher. Rainsford makes the Malay mancatcher by attaching a protruding bough, which acts as a trigger, to a large dead tree that is resting precariously on a smaller tree. When the general circles back around in search of Rainsford, he steps on the protruding bough and the dead tree immediately crashes to the ground. The tree injures the general by glancing off his shoulder but he survives the trap. After suffering his shoulder injury, the general congratulates Rainsford on making a Malay mancatcher and announces that he will have his wound dressed before he continues the hunt.

Rainsford manages to hurt Zaroff just a little bit by setting a trap for him.

Specifically, Rainsford uses a big tree that is leaning on a little one.  We are not told exactly how he manages it with only a knife as a tool, but he is able to make it so that the big tree will fall when Zaroff touches a trigger (a protruding branch).  Zaroff touches the trigger and the tree falls.  But Zaroff is quick enough and is paying good attention so the tree only hits his shoulder a little.

What does the passage suggest about Rainsford's character in "The Most Dangerous Game"?

"I will not lose my nerve. I will not.
He slid down from the tree, and struck off again into the woods. His face was set and he forced the machinery of his mind to function."

For the first time in his life, Rainsford is truly afraid. He's being hunted by Zaroff just as Rainsford as hunted big game animals all of his life. He is now the prey, and this thought has caused him to doubt if he can win Zaroff's "game". When Rainsford speaks these words aloud, it shows his determination to beat Zaroff and survive. He forces himself to think rather than panic. Because Rainsford is an experienced hunter, he knows panic is his worst enemy, so he forces himself to use the "machinery of his mind" to analyze his situation and come up with a plan. He's an intelligent man who realizes the only way to beat Zaroff is to outthink him.

It sounds as if he does sometimes question his own abilities. However, his internal self is able to reassure him that he will not fail and become afraid. He does have some self-doubt. Since he has no one available to talk to about his fears, he can and does engage in self dialogue. In psychology, this is a common occurrence to bolster one's self and find the courage to succeed. Only someone with a good self-esteem can use this tactic.