what does buck triumph tell the reader after he becomes leader of the dog team?

Do you mean his triumph over Spitz? This tells us that Buck has what it takes to be an alpha dog among the team.

I meant over Perrault and Francois

Buck doesn't really triumph over Perrault and Francois. They are men and in charge of dogs, even Buck. They certainly see that Buck is the strongest and most dominant dog: that's why they make him lead dog.