Spitz is Buck’s last steppingstone on the way to becoming Buck, Master of the Universe. He may have conquered snow, starvation, and the need to wear little dog shoes, but Buck isn’t there until he has it out with Spitz.
Because Spitz needs to go down in the end, it’s helpful that we don’t like him. He’s cruel and pugilistic (meaning he’ll start a fight with you if you so much as accidentally breathe on him):
Spitz was equally willing. He was crying with sheer rage and eagerness as he circled back and forth for a chance to spring in. (3.4)
When he goes up against our noble and determined protagonist, we all know who’s going to win...but we're still on the edge of our seats because this match is pretty even. Spitz's a worthy adversary for our Buck:
It was inevitable that the clash for leadership should come. Buck wanted it. He wanted it because it was his nature, because he had been gripped tight by that nameless, incomprehensible pride of the trail and trace--that pride which holds dogs in the toil to the last gasp, which lures them to die joyfully in the harness, and breaks their hearts if they are cut out of the harness. [...] This was the pride that bore up Spitz and made him thrash the sled-dogs who blundered and shirked in the traces or hid away at harness-up time in the morning. Likewise it was this pride that made him fear Buck as a possible lead-dog. And this was Buck's pride, too. (3.23)
So Spitz’s presence is at least partly responsible for two main themes in this novel: inevitability and competition. As we mentioned, it's inevitable that 1) Spitz will fight Buck, and 2) Buck will win and take his rightful place as leader of the pack.
The competition part is equally clear; this is the classic alpha dog meets alpha dog scenario.