In White Fang, competition appears in its most old-school, biological sense. Here it means fighting over food, resources, and in many cases, the ability to go on living. When you're fighting for your life, you're usually fighting against something specific: wolves, lynxes, that jerk with the chain and the club, or a murderous murderer. White Fang starts competing when he's just a puppy and doesn't stop until the very end of the book. It's pretty much who he is, and the fact that he's good at it is really the only reason he's still alive.
Competition is as much a part of the civilized world as it is in the wild. The only thing that changes is the stakes.
Competition doesn't really exist in the civilized world, which is what makes California such a nice relaxing place for White Fang.