The targeted player having more life than the current player is a part of the targeting requirement. A player can’t be targeted by this ability unless it’s true, and the ability doesn’t resolve if it’s no longer true at that time.
At the beginning of each player's upkeep, that player chooses target player who has more life than they do and is their opponent. The first player may have this enchantment deal 1 damage to the second player.
The ability can only target an opponent of the current player.
