There are actually a couple directions you could go with this question, for there are two major parallelisms in the story. First, there is that between life and fire. When old Koskoosh is abandoned by his tribe, as per tradition, he is given a small pile of firewood to keep him warm for a short time; after this fuel runs out he will presumably freeze to death. London writes that “At last the measure of his life was a handful of fagots. One by one they would go to feed the fire, and just so, step by step, death would creep upon him.” As the fagots burned away, Koskoosh relived memories from his early life; here was a physical measure of the remainder of his life—the fuel for the fire—running against a psychological measure of his life as he had lived it—his memories. As the fire slowly eats away at the wood, so do our experiences slowly eat away at the time we have on earth; as the ashes serve as a memory of the burning fire, so do our memories serve as the ashes of our youth. And at the end of the story, when Koskoosh purposefully extinguishes the fire, he knows also that he is purposefully extinguishing his life.
The second parallelism is that between Koskoosh and the old moose he recalls from his youth—this moose was taken down by wolves, though not without a fight. And as Koskoosh sits in the snow, he hears the nearby howling of a wolf; all of a sudden “the vision of the moose” comes back to him—“the torn flanks and bloody sides, the riddled mane, and the great branching horns, down low and tossing to the last.” Here he sees a new fate—his own, abandoned to the hunger of the wolves. Koskoosh sees himself in that old bull, abandoned by its own tribe to fend for itself against the wolves so many years ago, and he knows from this experience that it is his lot in life—his role in the grand scheme of nature—to become prey to the pack. “What did it matter after all?” he reflects, “Was it not the law of life?” His own end runs parallel to that of the old moose; neither life is sacred, and the vast expanse of the universe could care less about what happens to either of them—“it was the same everywhere, with all things.” Man or beast, they all tread the same path, and confront the same fate.
In the story, the parallelism of the dead of Old Koskoosh, old moose and old men means all things on earth must follow the same law. Life gives both men and animals different roles, but when all is said and done, everything eventually dies. The "law of life" and life itself can be wonderful but at the end the "law of death" must be obeyed. That is why Old Koskoosh gives in to the wolves at end of the story. He remembers leaving his own father on the ice and realizes it is time for him also to die.