"They got Bill, an' they may get me, but they'll sure never get you, young man," he said, addressing the dead body in its tree-sepulchre. (3.21)
Competition, part the first: Henry sets the stakes of his battle with the wolves. If they get the coffin, they win. If he keeps it safe, he wins. Notice that he no longer cares about his chance at living: he's pretty much already given that up to the wolves. He sets his own terms for the engagement, unlike animals, who compete only for food and the ability to go on living. (Animals probably have it a little rougher.)
But if they were all mildness toward her, they were all fierceness toward one another. (4.13)
We're dealing with sex here, but not the NSFW kind. Sex in White Fang is all about the ability to procreate, and pass your genetics on to another generation. It's a huge deal, which is why the fight here ends up being a fight to the death. And you thought having to pay for dinner was bad…
His development was in the direction of power. In order to face the constant danger of hurt and even of destruction, his predatory and protective faculties were unduly developed. (11.12)
London equates power with the ability to thrive in competition. To fight, to win, to survive… that's apparently all White Fang is good for, at least at this stage.
In reality it took away from him all honour, and instead of being bully and master of the pack, he now found himself hated and persecuted by the pack. (13.5)
Sometimes, when you win, you lose. If you beat up all the other members of the pack, you become the pack leader. That's victory by competition, right? The only problem is, when you become the leader of the pack, you have to sit at the front of the sled team, being chased by the dogs you've already beaten up. Yeah, maybe you should have thought that one through.
Not for nothing had he been exposed to the pitiless struggles for life in the day of his cubhood, when his mother and he, alone and unaided, held their own and survived in the ferocious environment of the Wild. (13.24)
It sounds like London is pointing out the good side of competition. Fighting for his life every day makes White Fang a tough little bugger.
To be compelled to run away before the yelling pack, every dog of which, for three years, he had thrashed and mastered, was almost more than he could endure. But endure it he must, or perish, and the life that was in him had no desire to perish out. (15.2)
In this passage, the competition changes a little bit. He's not fighting against other dogs here. Well, okay, he's fighting against other dogs (who are chasing him and trying to kill him). But on a larger sense, he's competing against death, which is what all the other competitions in the story basically boil down to.
He never knew defeat. His early training, when he fought with Lip-lip and the whole puppy-pack, stood him in good stead. There was the tenacity with which he clung to the earth. (17.12)
Once again, early competition makes later competition easier. White Fang just doesn't lose. And that's a good thing too because losing means death and we still have eight or nine more chapters to go.
"I said don't break them teeth," the faro-dealer repeated more ominously than before.
But if it was a bluff he intended, it did not work. Scott never desisted from his efforts. (18.41-42)
This isn't a confrontation, but it's definitely a competition. Tim wants Scott to back off. Scott declines, making him the winner in the puffed-up-chest-and-menacing-noises phase of the proceedings.
He snarled more menacingly, crouched still lower, and still the hand descended. He did not want to bite the hand, and he endured the peril of it until his instinct surged up in him, mastering him with its insatiable yearning for life. (19.47)
The competition here is between man and wolf, but for the first time, there's something more than death at stake. Weedon's trying to recover White Fang's soul, and the battle of wills between them is about whether White Fangs trusts him. If he doesn't he'll be killed, but if he does, he'll be saved from all the hate and death surrounding him. Big stakes.
"I'll tell you what I'll do," he challenged finally. "I'll lock White Fang in with the chickens all afternoon." (23.23)
There's still competition in civilization, just much less dire. Well, it's pretty dire for the chickens, but for everyone else, it's more a matter of money and pride.