We doubt there are many people out there who would argue that The Two Towers isn't an adventure novel. We've got fighting, mayhem, danger, and secrecy on every page. And of course, what generates all of this adventure is the Ring quest, so the "quest" genre is a no-brainer, too (for more on this, check out our "Genre" page for The Fellowship of the Ring).
That leaves us with folklore. Sure, we admit that The Two Towers is not a direct or recognizable folktale. Still, it includes a lot of folkloric elements: elves, dwarves, magic rings, a deep sense of history, and the whole good-vs.-evil plot structure of course. Tolkien invents new folklore for the twentieth century by combining traditional fairy tales and epic narrative structure. The Two Towers provides us with folklore for a new, contemporary age.