Wuthering Heights is a Romantic novel because its hero and heroine, Cathy and Heathcliff, are unconventional. Heathcliff is a former street urchin who is born without connections, and Cathy loves him in spite of her marriage to the better connected Edgar Linton. Heathcliff is the quintessential Romantic hero, in the tradition of Goethe and Byron, as he is alienated from society and misanthropic. He has a dark character and is prone to obsessions, such as his love for Cathy. This type of love is transcendent in the Romantic tradition, as it is greater than class barriers, geographic distances, and even death.
Another element of the novel that is Romantic in nature is the solace and release that nature provides to Cathy and Heathcliff. They often gather on the moors as children to experience the kind of freedom that they can't enjoy indoors, and Heathcliff seems like a creature who is more connected to nature than to civilization. It is only outdoors and in nature, with all of its moods and storms, that they can find true freedom.
In addition, the novel places an emphasis on the beauty and inspiration of childhood. During childhood, Cathy and Heathcliff are first drawn to each other, and then adulthood imposes uncomfortable strictures on them. They both yearn for the love, freedom, and beauty that they experienced as children.