The word 'romance' isn't a reference to the covert or overt displays of sexually-suggestive affection we are familiar with today. Rather, the term references the 18th/19th Century Romantic movement encompassing literature, art, and music. This movement saw the relaxing of strict rules in poetry, prose, and art forms. The imagination (subjective) was elevated above classicism and realism.
So, the sentence above refers to Vera's gift for making up elaborate and imaginative stories on short notice. She is the type of person who can make up a fantastic story on the spot. Her mischievous sense of humor allows her to concoct a wild tale of morbid terror to horrify the gullible Framton.
After she finishes the gothic tale of disappearance and mysterious deaths, the subjects of her story turn up very much alive. Framton is so spooked that he makes a run for it.
"A most extraordinary man, a Mr. Nuttel,” said Mrs. Sappleton; “could only talk about his illnesses and dashed off without a word of good-bye or apology when you arrived. One would think he had seen a ghost."
In response to Mrs. Sappleton's comment, Vera makes up another fantastic story to explain Framton's sudden departure. Her penchant for imaginative story-telling immediately designates her a romantic who derives great pleasure from her skill.