I am sure other editors might disagree with me but I don't actually think this story has much to do with "haunting" in the traditional oh-no-there's-a-ghost-behind-you kind of way. The principle theme of this incredible short story is one woman's account of her own mental condition and how this spirals down and down until she reaches a point of complete insanity. We need to be aware of the way in which the female narrator is unreliable, and we need to see how she projects her feelings of despair, entrapment and anger in the curious yellow wallpaper in her room.
Note how as the narrative progresses she sees a woman in the wallpaper, who moves around and "shakes" the bars of the yellow wallpaper:
The front pattern does move--and no wonder! The woman behind shakes it!
...Then in the very bright spots she keeps still, and in the very shady spots she just takes hold of the bars and shakes them hard.
And she is all the time trying to climb through. But nobody could climb through that pattern--it strangles so; I think that is why it has so many heads.
What we come to realise is that this woman that she sees in the wallpaper is her own intellectual and emotional self that is "trapped" and "encaged." Although her husband means well and is following the orders of the doctor, she is not allowed to escape or to express herself, and thus she eventually gives in to insanity.
Thus whilst there is a supernatural presence in the wallpaper, we can identify that it represents the anger and rage of the narrator who is forced to lie in silence on a bed in this room, imprisoned and encaged just as surely as the woman that she sees raging so strongly against her captivity.
If one employs the one denotation of haunt, to intrude upon continually as an idea "haunts" a person's mind, then readers may certainly perceive the narrator of Gilman's "The Yellow Wallpaper" as haunted by the sickening yellow paper on the walls of her confinement, a wallpaper that seems to take on expression and give perverse form to itself in its asymmetry.
This wallpaper, in its haunting presence for Gilman's narrator, seems "a strange, provoking, formless sort of figure, that seems to skulk about behind that sill and conspicuous front design." To the narrator, therefore, the figure that she perceives--whether it be real or in her mind--assumes the characteristics of a veritable ghost as it becomes
like a woman stooping down and creeping about behind that pattern. I don't like it a bit. I wonder--I begin to think--I wish John would take me away from here!