While at first glance it would seem that a gruesome story like "Fall of the House of Usher" has no Romantic qualities, if you look at a couple of the elements of Romanticism, it is easier to see how the story fits into the literary era. Here are several Romantic elements and how Poe's story uses them:
1. Gothic style--The Gothic style in America became popular during the Romantic time period. Poe and Hawthorne are great examples of authors who wrote Gothic works. Several features of the Gothic style are a mysterious setting (think of the Usher house with its underground burial crypt), death or premature burial (think of Madeline in the story), and exotic elements (as the reader, you don't really know where the Usher house is, but it makes readers think of a castle-type structure or fortress, possibly in Europe).
2. Supernatural or unrealistic elements--the Romantic authors believed strongly in using their imaginations; so their works are not realistic and include elements of the supernatural. In this Poe story, the idea that Madeline just happened to have a condition where she went into a coma-like state and ends up being buried alive while the narrator is visiting is highly unbelievable, but it works to help Poe's plot; so readers would have expected elements such as this. Another example of this Romantic quality of supernatural elements is the destruction of the house in the storm at the same time that Roderick Usher dies. The Usher house is destroyed as the same time as the House of Usher (the Usher bloodline)--interesting, but too coincedental for a realistic story.
3. Dark Romantic authors like Poe believed that man was born basically evil, and that humans must struggle their whole lives to keep their evil nature from overtaking them. In this story, Roderick is in a battle against the powers of evil (psychological issues and his sister who is not in control of herself).
4. Symbolism--Romantic authors rely heavily on symbolism. In "Usher," the narrator mentions a "fissure" (a crack) in the foundation of the Usher house. While that is a literal crack or fracture, it is also symbolic of the "cracks" in the Usher family. The last Ushers--Roderick and Madeline--are flawed just like the house, and therefore neither can survive.
I hope that this helps you. I know that these literary styles such as Romanticism and Realism and Modernism can be rather confusing at first.