Gothic themes can include horror, terror, the supernatural, spiritual, melancholy, and the imaginary. In "The Haunted Mind," the narrator contemplates a realm between sleep and being awake. He is fascinated with the space/time between dreams and the conscious life. It is magical to him. Likewise, he considers this in strict terms of time (temporal), when it is neither yesterday nor tomorrow.
You have found an intermediate space, where the business of life does not intrude; where the passing moment lingers, and becomes truly the present a spot where Father Time, when he thinks nobody is watching him, sits down by the way side to take a breath.
This is supernatural, transcendent, or metaphysical at least since it is a space/time that is out of or above time, a space where/when "mortals live on without growing older!"
The narrator muses on staying in bed forever, perhaps trying to revel in the afterthoughts of his previous transcendent state. But then he segues from this concealed state in bed to the confinement of a grave. Here is the incursion of horror, another Gothic theme. Now, still in a slightly dreamlike wakefulness, he imagines or sees a funeral procession gliding passed (he says "your" - to the reader) his bed. This train comes with personified feelings of Disappointment, Fatality, and Remorse.
He wakes out of this half asleep-half awake nightmare and then proceeds to attempt a more pleasant state induced by the soft breathing of someone he might sleep next to. Again, this is a (much more pleasant) state of the fine line between wakefulness and sleep. When he foresees deep sleep, he compares it to a temporary death and supposes the final death will be as calm.
This story plays mostly with Gothic themes of dreams, appearance vs. reality, but also delves into death and nightmares.