Here the words "he" and "his" refer to Christ.
"he will stop those people who rule, who have authority, and who have power from doing what they are doing"
Kings who won wars would put their feet on the necks of those whom they had defeated. AT: "until God has completely destroyed all of Christ's enemies" (See: rc://en/ta/man/translate/figs-idiom)
Paul speaks of death here as if it were a person whom God will kill. AT: "The final enemy that God will destroy is death itself" (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-personification)