"Sir Gwain and the Green Knight" is a medieval romance but is by no means a love story.
In the 14th century when this tale was written romances were broadly defined as very imaginative literature set in a fantasy world that features a battle between good and evil. More specifically they need to have an almost perfect hero, a long and dangerous quest, supernatural elements and a female figure of some sort. The story of "Sir Gwain and the Green Knight" meets all of these characteristics and is therefore a medieval romance.
The key elements that make a story a medieval romance are imaginative literature, fantasy world setting and a battle between good and evil. All of these elements are demonstrated by Sir Gwain himself when his New Year's dinner with King Arthur and a few other knights is interrupted by a green stranger who proposes a "game". The strange green knight asks if someone will exchange a blow for blow and Sir Gwain is the only one to accept. Sir Gwain swiftly chops the Knights head off as requested but to everyone's surprise. The Green Knight ".held his head in his hands up high before him" (28). The knights headless body lept onto his horse "And the eyelids lifted wide, and the eyes looked out/And the mouth said just this much, as you may hear now" (30-31). He then challenged Sir Gwain to keep his promise by finding the Green Chapel in one year and receive his below. This scenario illustrates a fantasy world because obviously in the real world nobody can hold up their decapitated head. It is also an example of good vs. evil because the honorable Sir Gwain is having his life threatened by a sneaky stranger.
The hero traveling on a long and dangerous quest is another essential part of any medieval romance. This key element is present in "Sir Gwain and the Green Knight" when Sir Gwain "shaved through the heavy thicket grown up by the woods/and rode down the steep to the floor of the valley" in order to find the Green Chapel.