I play this card while DigiXrosing with 2 cards, but there are no cards with [Knightmon] in their name, [DeadlyAxemon], or [Nene Amano] among the cards revealed by the [On Play] effect.Does the "delete 1 of your opponent's Digimon with a play cost of 4 or less" effect still activate?

What does this card's (Rule) mean, exactly? (*This card's "The name of this card/Digimon is also treated as [SkullKnightmon] and [DeadlyAxemon]" has been changed to "(Rule) Name: Also treated as [SkullKnightmon] and [DeadlyAxemon].")