On page 59 the excerpt reads as follows: ",,,but the strange dog, no matter what the breed valor, swiftly acknowledge Buck's supremacy or found himself struggling for life...." What does supremacy and valor mean?

This quote directly relates to dogs that challenged Buck while he was with Thornton. It didn't matter how tough the dog was, or how courageous, Buck was supreme... the leader of the pack.

In context....

His face and body were scored by the teeth of many dogs, and he fought as fiercely as ever and more shrewdly. Skeet and Nig were too good-natured for quarrelling,—besides, they belonged to John Thornton; but the strange dog, no matter what the breed or valor, swiftly acknowledged Buck’s supremacy or found himself struggling for life with a terrible antagonist. And Buck was merciless. He had learned well the law of club and fang, and he never forewent an advantage or drew back from a foe he had started on the way to Death.