First, we need to identify the major theme of Stevenson's novella The Strange Case of Dr. Jekyll and Mr. Hyde, then second, pin point central features of Gothic literature to see which might be reflected in the theme. It is good to note that Dr. Jekyll and Mr. Hyde is recognized as Romantic Gothic literature.
The central theme of Stevenson's story is how identity is affected by the duality of good and evil. Jekyll is fully aware of the duality within himself. Jekyll, on the one hand, loves the respect of his peers and friends and, on the other hand, enjoys a little wickedness in behavior. If this duality were known about, it would sully his reputation. The deeper duality ("deeper trench") came in Jekyll's need to appear to have only one side to his nature, not two:
from the high views that I had set before me, I regarded and hid [my irregularities] with an almost morbid sense of shame.
Since his struggle with shame over the appearance of a divided self affected his happy participation in either good or evil, he dreamed of a way to operate as two separate people.
I had learned to dwell with pleasure, as a beloved daydream, on the thought of the separation of these elements. If each, I told myself, could be housed in separate identities, life would be relieved of all that was unbearable
It is to the fulfillment of this dream that his research in metaphysical and transcendental medicine eventually led, resulting in the birth of Mr. Hyde.
Gothicism was originated with Walpole in England in 1765, a little ahead of the origination of Romanticism with Goethe in Germany in 1774. [It is of interest that Goethe later renounced the Romantic movement and the first Romantic novel The Sorrows of Young Werther when he saw a young woman pulled from a watery grave in a semi-frozen river with a copy of Young Werther in her skirt pocket.]
Romanticism's dark side embraced Gothicism as is evidenced by Romantic era works like The Rime of the Ancient Mariner (Coleridge), Jane Eyre (Bronte) and Frankenstein (Shelley). As these titles illustrate, two prominent features of Gothic literature are the duality between good and evil along with death and dying.
Therefore, the features of Gothic literature reflected in the major theme of Dr. Jekyll and Mr. Hyde are the Gothic consciousness of humanity's inner battle between impulses of good and evil and a fascination with the process of dying and the possibly judgmental nature of death as seen in Hyde/Jekyll's demise.