What did white fang achieve by following the law

He achieved a covenant between himself and his man.

"The months went by, binding stronger and stronger the covenant between dog and man. This was the ancient covenant that the first wolf that came in from the Wild entered into with man. And, like all succeeding wolves and wild dogs that had done likewise, White Fang worked the covenant out for himself. The terms were simple. For the possession of a flesh-and-blood god, he exchanged his own liberty. Food and fire, protection and companionship, were some of the things he received from the god. In return, he guarded the god’s property, defended his body, worked for him, and obeyed him.

The possession of a god implies service. White Fang’s was a service of duty and awe, but not of love. He did not know what love was. He had no experience of love. Kiche was a remote memory. Besides, not only had he abandoned the Wild and his kind when he gave himself up to man, but the terms of the covenant were such that if ever he met Kiche again he would not desert his god to go with her. His allegiance to man seemed somehow a law of his being greater than the love of liberty, of kind and kin."