Your opponents can't gain life.
At the beginning of each end step, each opponent loses life equal to the life that player lost this turn. (Damage causes loss of life.)
Archfiend of Despair’s last ability counts only how much life was lost. It doesn’t care whether a player also gained life.
The amount of life to lose is determined only as Archfiend of Despair’s triggered ability resolves. For example, if you control two of them and an opponent lost 3 life earlier in the turn, the first ability to resolve would have that player lose 3 life, and the second would have that player lose 6 life.
In a Two-Headed Giant game, damage and life loss happen to each player individually. If each player on a team is dealt 2 damage, each of those players loses 2 life and the team’s life total goes down by 4. When Archfiend of Despair’s ability resolves, each of those players again loses 2 life and the team’s life total goes down again by 4; they don’t each lose 4 life.