The "tenderfoot" approaches the trip in the hostile Arctic wilderness with the arrogance of man separated from nature; he is convinced that his intellect will get him where he wants to go, even though he has no experiential knowledge of the conditions he will face. The dog and old-timer are different. Because of his nature and his experience in the wilderness, the dog knows that the man does not belong there and that it cannot work out. He even knows through some natural instinct that the man would kill him to save himself, and backs off to save himself. The old-timer doesn't have the dog's instinctual knowledge, but he has experiential knowledge; he has a respect for the natural world that the tenderfoot does not, built on years of experience in the conditions.
The tenderfoot could have saved himself by paying attention to the old-timer, but he did not, so he is a foil in that regard. The dog is the vehicle that London uses throughout the story to keep us "up to date" on the ever devolving situation of the tenderfoot; the dog's actions/comments tell us how someone in true contact with nature would have reacted were he not so arrogant.