In London’s book, the character Avis writes, “The great driving force of the oligarchs is the belief that they are doing right. Never mind the exceptions, and never mind the oppression and injustice that they are doing right. . . . All is granted. The points that the strength of the Oligarchy today lies in satisfied conception of its own righteousness.” What does London mean by that commentary through his protagonist?

Avis means that people convince themselves that they're doing the right thing; even if they're hurting others, people take action not because they see themselves as evil, but rather because they justify their own actions through some kind of internal logic.
Avis is explaining that the Oligarchy—the Iron Heel—believed that they were the protectors of humanity against the evils of socialism and the rule of the lower classes. They believed themselves to be heroes defending their people and country against anarchy. She says:

They, as a class, believed that they alone maintained civilization. It was their belief that if ever they weakened, the great beast would ingulf them and everything of beauty and wonder and joy and good in its cavernous and slime-dripping maw. Without them, anarchy would reign and humanity would drop backward into the primitive night out of which it had so painfully emerged. The horrid picture of anarchy was held always before their child's eyes until they, in turn, obsessed by this cultivated fear, held the picture of anarchy before the eyes of the children that followed them. This was the beast to be stamped upon, and the highest duty of the aristocrat was to stamp upon it. In short, they alone, by their unremitting toil and sacrifice, stood between weak humanity and the all-devouring beast; and they believed it, firmly believed it.

This moral imperative props up the ability of the Iron Heel to do terrible things to people. Behind each of their actions is the justification that if they didn't do that thing, something worse would happen. 
When the Iron Heel betrays its treaty with Germany, for example, it frames the betrayal by saying they were doing it so that America—the country of the Iron Heel—could sell its own surplus on the world market. Even though it led to the emperor being deposed, they didn't see their own actions as bad; rather, they saw it as a clever move designed to create a better situation for their own country.
She explains that the Revolution also believed in their own righteousness, which explained their actions. People were tortured to death, for example, but still refused to betray others in the cause. In the same way that their sense of righteousness is the Oligarchy's strength, so is it the strength of the Revolution. 
Ultimately, Avis is saying that most people believe they are doing the right thing—even when it is clear that they aren't, such as with the actions of the Iron Heel. Jack London uses this explanation to show the motives behind the Iron Heel's terrible actions and to explain how they could justify those choices.