Symbolism, Imagery, Allegory
When Stevie sees a cabman whipping a horse, he freaks out so badly that it almost seems as if the man is whipping him. In this way, animals play an important part in this book because they represent living things that are capable of feeling pain, but are not treated with human compassion.
Similarly, Stevie isn't considered fully human by Mr. Verloc, who extends him "as much recognition [...] as a man not particularly fond of cats may give to his wife's beloved cat" (2.138). Burn, Verloc. Who doesn't like a nice kitty?
Verloc's neglect for Stevie eventually leads to the boy's death. But hey—justice gets served to Verloc on the end of a carving knife. Take that.
Through animals, Conrad represents humanity's ability to be cruel without considering the feelings of others. However animals also represent how cruelty is caught up in a cycle that is difficult to stop. For example, after Stevie gets upset with the cabman for whipping his horse, the cabman replies that "This ain't an easy world" and goes on to talk about how awful his life is compared to the horse's.
The narrator actually backs him on this earlier in the chapter, saying that the man whips his horse "not because his soul was cruel and his heart evil, but because he had to earn his fare" (8.28). In a capitalist world, there'll always be people who have to scrape for whatever little they can get, even if it means being cruel to others. It's not only dog-eat-dog, it's man-whip-horse.