“Shape of You” is sung by a male in the 1st person point of view, which does not line up with Radway’s model of a heroine-centric story.
“Come on now, follow my lead/I may be crazy, don’t mind me/Say, boy, let’s not talk too much…come on now, follow my lead”–Here, the hero tells the heroine to follow his lead, which matches a few qualities of Radway’s ideal romance hero (independent, demanding, experienced in relationships). However, the heroine answers by telling the hero to follow her lead as well, which suggests that the two are equals in the relationship. Radway would interpret this as the heroine finding her own self-actualization within a romantic relationship.
“Although my heart is falling too/I’m in love with your body”–These lines show that the hero is mainly attracted to the heroine sexually, though his “heart is falling too.” This relates to Radway’s 4th element of an ideal romance, in which the heroine believes that the hero is purely interested in her sexually because the hero does not reveal his true feelings. However, this level of attraction does not cause conflict between the couple like it does in Radway’s romances.
“We talk for hours and hours about the sweet and the sour/And how your family is doing okay/Leave and get in a taxi, then kiss in the backseat”–These lines could be interpreted to match up with elements 11 and 12 of Radway’s ideal romance. The act of taking the heroine on a date and discussing her family shows that the hero is committed to starting a relationship with her. After the date, the two kiss, which represents a sexual and emotional response from the heroine. However, these actions are less intense than the usual plot points in Radway romance novels, which would most likely include a proposal of marriage and full sexual intercourse.
Since the hero and heroine are in a mainly sexual relationship that never experiences conflict or resolution, Radway would not consider “Shape Of You” a romance.