It doesn't need to say "or" because the target has to match all three descriptors, non-werewolf, non-zombie, AND non-vampire. The card has only one instance of the word "target" and doesn't specify a number, so it destroys one creature by default.
You target only a single "non-Vampire, non-Werewolf, non-Zombie creature" (note the singular word "creature"; compare with Nekrataal). This means that the creature you target can't be a Vampire, Werewolf, or Zombie. If the spell said "non-Vampire, non-Werewolf, or non-Zombie creature", a creature would be excluded from that description only if it had all three creature types.
EDIT (Apr. 27; Dec. 20, 2017; Mar. 8, 2019): Correctness edit.