When two cards with the same nemesis icon are in play, all damage they do to each other is increased by 1. It does not matter whether the two cards are both villain cards, both hero cards, or anything else. That means, in particular:
  • The Chairman and The Operative get nemesis bonus damage against one another
  • The members of The Ennead get nemesis bonus damage against each other
  • The members of The Sentinels get nemesis bonus damage against each other
Most of the time you don't see it happen, because villain cards don't usually deal damage to villain targets. But if damage is redirected, the source of the damage remains the same, and so a nemesis bonus can apply. For example, you can use NightMist's Amulet of the Elder Gods to redirect damage from The Operative to The Chairman (with a nemesis bonus). It's actually a great strategy, because The Chairman will then hit The Operative back (with a nemesis bonus).

Note: a card dealing damage to itself does not get a nemesis bonus.