Extinguisher Battleship failing to destroy support cards with no opponent´s creatures in play

Keyler

I was playing "Extinguisher Battleship" into some decks and I think does not work when opponent has one or more supports in play but no creatures. Seems like if its second effect "Then, do 4 damage to each opponent's creature" doesn´t have objetives, its first effect "destroy a random opponent´s card" also fail.
This shouldn't happen because the main effect is to destroy something of the opponent, so the secondary effect shouldn't affect it.