You have it backwards.

This formal game-theoretic notion of fairness acknowledges that power disparity exists and that having less power than your counterparty allows them to inflict greater disutility on you without you being able to inflict disutility on them in turn to discourage this.

On the other hand, fairness "in the usual sense", pretends power disparity doesn't exist and that, say, an armed robber is not allowed to take your stuff when you have nothing to defend yourself with. Which in reality only works as long there is a powerful third party (the state) that will inflict disutility on the robber for it.