Mary Howitt wrote the poem "The Spider and the Fly."
This is a moral fable told with great good humor, depicting a common human weakness. The spider extends a cordial invitation to his potential victim...The fly, well aware of the danger, fends him off until he appeals to her vanity.
To identify whether the poem is Gothic, one needs to understand the characteristics of this kind of literature:
Gothic literature [was] a movement that focused on ruin, decay, death, terror, and chaos, and privileged irrationality and passion over rationality and reason...
Gothic literature often has a connection to things medieval, and frequently this includes a damsel in distress. Many times there is an element of the supernatural. It is not unusual that the setting is in a far away, unfamiliar place. The mood is often dark, gloomy and/or ominous.
…the Graveyard School of poetry [was] so called because of the attention poets gave to ruins, graveyards, death, and human mortality…
In terms of the poem, look the imagery.
We see the theme of death in the following lines:
Oh no, no, said the little Fly, to ask me is in vain,
For who goes up your winding stair, can ne'er come down again.
The theme of death is found in these lines as well:
Oh no, no, said the little Fly, for I've often heard it said
They never, never wake again, who sleep upon your bed!
The author's reference to the spider's "den" may allude to a lion's den, another place of danger and death.
Images of ruin and decay can be found when the spider invites the fly to his pantry:
I've heard what's in your pantry, and I do not wish to see!
The reader can infer, with the knowledge of a spider's activity, that his pantry might be filled with the dead carcasses of other less fortunate insects.
It is safe to infer that this next segment has the sound of the supernatural. (Supernatural here does not refer to ghosts, but to anything that is beyond the realm of the natural world.) The allusion is much like that in the mythological tale of the sirens in The Odyssey who lured sailors to their deaths upon the rocks, while these creatures sang tunes that mesmerized their victims—those who could not resist the music:
Come hither, hither, pretty Fly, with the pearl and silver wing,
Your robes are green and purple, there's a crest upon your head
Your eyes are like the diamond bright, but mine are dull as lead!
The story is meant to point out the dangers of giving into things that appeal to one's vanity.
The unfamiliar territory of the spider's den is classic to Gothic literature. In this poem, the damsel in distress is the fly. Elements of decay and death are found in the imagery. Like Mary Shelley's Frankenstein and Walpole's The Castle of Otranto, the protagonist has a flaw that brings about destruction and death (in the poem's case, the fly's undoing is her vanity), and there is an element of the supernatural as well, as seen in the spider's ability to draw the fly against her better judgment.
While there is humor in the poem, there is darkness in that the spider is a predator, the fly knowledgeable but foolish. Imagery supports the sense of impending doom. There are elements of Gothic literature such as death, decay and ruin.