What is the "other fire" and who is the "other man"?

The "other fires" were meant as a distant time in the past when Buck's ancestors did the same things as Buck with other men. The fires represent Buck's hereditary past and dogs' connection with man.

Far more potent were the memories of his heredity that gave things he had never seen before a seeming familiarity; the instincts (which were but the memories of his ancestors become habits.