how does the man and the dogs fate contribute to the overall meaning?

I think a motif of the story is that instinct is superior to Knowledge. Jack London specialized in stories about the wilderness. His running theme involved the raw majesty and power of the elements. Naturalism was London's mantra and this story is a perfect example of this. In "To Build a Fire" the setting is in the Yukon. Unlike the man, the dog has instinct built into his DNA. The man's knowledge is subject to his pride and hubris. The dog and nature are in sync. The dog has been conditioned by generations of evolution and he instinctively understands what to do and when to do it. The dog also has the genetics (has fur) to survive better than man.