Here "the world" is a metonym for all the people in the world. See how these words are translated in [Psalms 9:8](../009/008.md). Alternate translation: "He will judge all the people of the world righteously" (See: [[rc://en/ta/man/translate/figs-metonymy]])
The words "he will judge" are understood. Alternate translation: "he will judge the peoples with his faithfulness" (See: [[rc://en/ta/man/translate/figs-ellipsis]])
The can be restated to remove the abstract noun "faithfulness." Possible meanings are 1) Alternate translation: "fairly, according to what he knows is true" or 2) Alternate translation: "using the same standard for all people" (See: [[rc://en/ta/man/translate/figs-abstractnouns]])