Inflicting damage and removing the monster use the same chain link.
You do not inflict damage when you remove from play DARK Monster Tokens or Trap Monsters are removed from play. However, you do inflict damage when a DARK Monster (which is being treated as an Equip Card) is removed from play.
This is a Trigger Effect which targets. Removing the monster and inflicting damage are considered to occur simultaneously.
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
↑Konami Judge Program Rulings are considered unverified, as their source(s) are not publicly viewable. They are not confirmed as applicable to the TCG until they have been officially published by Konami.