This poem contains the supernatural in the form of the actual "listeners" that the poem is named after. In the poem, a traveller comes riding up to a cottage in a forest, "knocks on the moonlit door", delivers a message, then leaves. But, the entire time, the author describes some strange presences that are on the other side of the cottage door, and how they throng there, listening quietly to the man outside. Walter de la Mare describes the listeners as a supernatural presence:
"But only a host of phantom listeners/That dwelt in the lone house then/Stood listening in the quiet of the moonlight/To that voice from the world of men:/Stood thronging the faint moonbeams on the dark stair."
In this passage, the listeners are described as phantoms that dwell in the moonlight, that are not part of the world of men. They are a supernatural presence-phantoms or ghosts of some kind. Later, it mentions that the traveller "felt in his heart their strangeness." It is interesting that even though they do not make a noise, or go swirling around him or hurling butcher knives at him like they tend to do in movies, the traveller can still feel their presence; he knows that they are there. So they aren't totally absent-they have a palpable presence. In fact, he can sense them so strongly that he trusts them with his very important-although ambiguous-message, that he kept his word. He leaves that message with them, and leaves.
So, the supernatural in this poem exists in the form of an entire host of phantoms, who aren't part of the normal world of men, but that can be sensed. They are a main character in the poem, one that can listen, can be trusted with messages, that move forward to receive the message and disappear "softly backward" when they have received it. The author leaves a lot to the imagination, not explaining things, allowing you to fill in gaps as you may, to make this supernatural presence whatever you might infer it to be.