Crimson Honor Guard's last ability triggers at the beginning of each player's end step whether that player controls a commander or not. Whether that player controls a commander is checked only as the ability resolves.

Crimson Honor Guard will deal 4 damage to you, too, if you don't control a commander.

The player could control any player's commander to satisfy Crimson Honor Guard's ability. If a player gains control of another player's commander “until end of turn,” the player who gained control of it will still control that commander during the end step.