Rainsford is an experienced hunter. In fact, he is a world-renowned hunter, who has hunted around the world. For this reason, he has learned tips from different parts of the world. For example, he used a Malay trap to wound Zaroff. Zaroff is impressed and even congratulates him.
In order to kill the dogs that were pursuing him, Rainsford remembered what he learned in Uganda. This was perfect timing, as the dogs were in hot pursuit. So, Rainsford slid down the tree and got a green branch and tied his hunting knife to it. He knew that as the dogs would come, they would spring the trap. He was right. The barking of dogs stopped; the assumption is that they died. All of this shows that Rainsford is an accomplished hunter who is able to think off his feet. Here is the quote:
They would be on him any minute now. His mind worked frantically. He thought of a native trick he had learned in Uganda. He slid down the tree. He caught hold of a springy young sapling and to it he fastened his hunting knife, with the blade pointing down the trail; with a bit of wild grapevine he tied back the sapling. Then he ran for his life. The hounds raised their voices as they hit the fresh scent.