At the bottom, I have included two links, both of which provide good definitions and examples of Gothic literature or Gothic fiction.
The Black Cat is filled with elements of Gothic literature, as are most of Poe's other works. Ruins are common settings within Gothic literature, as are horror, death, and decay, among many other things. All of these things can be found in Poe's story. Horror overlays much of the narrator's tale, either his own horror at what he did or ours for the same reason. When his house burns down, it is left in ruins, which he later visits and sees an image of the cat he hung. That cat, Pluto, was the first death, which was eventually followed by his wife's murder at his own hands. Decay can be found at the end of the story, when his wife's body is discovered "already greatly decayed and clotted with gore."
There is one other element of Gothic literature that can be found in this story, but in a very interesting way. Gothic novels have an archetypal hero and villain (meaning they follow a pattern): the hero is usually isolated, and the villain is usually true evil, often because of implicit malevolence. I say that these archetypes appear in an interesting way because the narrator follows both rather than having two separate characters. At first, the narrator is isolated because he prefers animals to humans; but then a malevolence takes over him for no real reason and he takes to harming innocent creatures simply because he wants to.