While the wiki indicates that the Death Dealer is classified as a merchant, it doesn't specify teleporting to shops. If a shop is constructed in the room where the Death Dealer spawned, it typically doesn't count as being operated by the Death Dealer. The Death Dealer's functionality is primarily centered around providing items upon death rather than actively operating or teleporting to shops. It's recommended to refer to the specific game mechanics or developer documentation for precise details on the Death Dealer's behavior in your context.