Come on, you must seen this coming. Obviously, The Left Hand of Darkness is science fiction. Le Guin draws on scientific ideas like Einstein's Twin Paradox, alien cultures, and even pseudoscientific mumbo-jumbo like ancient astronauts. (Pro tip: ancient astronauts are not real.) There are space ships and devices that let someone talk from one planet to another. The works.
But most important, Le Guin draws huge inspiration from the field of anthropology—in fact her father Alfred L. Kroeber was a rather famous anthropologist himself. The story revolves around the struggles of Ai trying to understand and integrate himself within the Gethenian culture. His conflict is the same one an anthropologist faces each time she enters the field to do study. So, in a way, the science of Le Guin's science fiction is anthropology more than physics or astronomy (though they deserve their props too).
When people today think of stories labeled "Romance," they typically think of stories about love and lust and hunky men with torn shirts whisking off maidens to perform decidedly un-maidenly acts. Not so back in the day. Then, Romance was about knights and quests and maidens, sure, but maidens who needed saving from dragons more than tightly buttoned corsets.
The Left Hand of Darkness encompasses both aspects of Romance without fitting too neatly into either category. Like any knight of yore, Ai is on a quest to save a kingdom or, since this sci-fi, a planet. Unlike knights with shining armor, Ai's mission is not as easily categorized as "Here be dragons; go kill." Instead, Ai's opponent is the way his alien nature prevents him from navigating the ins-and-outs of Gethenian society, both in Karhide and Orgoreyn. Like a knight though, Ai must grow as a person to succeed in his task.
Like the Romances of today, The Left Hand of Darkness is a love story. Unlike a typical harlequin romance novel, it's not about creating contrived plots as an excuse for 100+ pages of graphic sexy-sex. Instead, Ai and Estraven fall in love with each other heart and soul, but never become physically intimate. The love story is a mature one, telling us about two people who defy the odds together and grow closer as a result. Okay, we'll admit it; the story's pretty sweet.
The Left Hand of Darkness as a whole isn't in the genre of Folklore, Legend, and Mythology. But certain chapters are. For example, Chapter 17 provides a mythological origin for the Gethenian race. Chapter 12 tells a couple of legends surrounding Meshe, the prophet of the Orgoreyn religion. And Chapters 4 and 9 give us little short stories in the form of Gethenian Folk tales—what they call hearth tales.
These supplemental chapters are like, well, supplemental vitamins. They aren't part of the main diet, but they round it out, give it a little more oomph. In The Left Hand of Darkness, these chapters give us a chance to dive deeper into the history and culture of Gethen and its people. They aren't necessary for us to understand Ai's story, but they are necessary for us to understand the book as a whole. So don't think you can skip them. You're being officially put on the honor system.