I think the appeal is in the thread title.
Tolkein/LotR is popular.
Put it this way I live in NZ...
I find it fascinating viewing this through the framework of those coming into the question thinking of D&D in terms of 5th edition, and thinking of LotR in terms of the movies...
The movies are popular, but the influence on the game goes back to the books. If one walks into a bookstore today and looks at the vast selection of fantasy novels available, one might not appreciate that such was not always the case. Back in the 60s and the 70s and even into the early 80s, LotR was not just the best fantasy available, it was the zeitgeist and the soul of fantasy. It created the fantasy genre and for a time (and still today, though not as directly) all fantasy was just a response to LotR. I remember reading the books for the first time (I was 9) back in 1982 and thereafter trying to write my own fantasy. I soon realized I was just trying to retell LotR. I was not alone. Terry Brooks readily admits (and its really obvious) that his first Shannara novel was just a reskinned LotR. That glut of fantasy novels and source material that we have today was not always there and is a direct result of people reading LotR for the first time and wanting to write fantasy. As more and more wrote, they began blending in from other sources, some of which predated Tolkien, such as fairytales and myths, but almost always they were building on the framework Tolkein had started.
Gygax incorporated Tolkien into Dungeons and Dragons, not just because it was popular, but because it was fantasy and, back in the day, fantasy was Tolkien. Tolkein's elves and dwarves and hobbits and orcs (goblins) and undead wizards leading armies was what we knew, and when we crafted our own stories, we were just expanding on his. Now its an intrinsic part of the legacy of the game.
One caveat - Before LotR, there was pulp fiction, and we cannot discount the influence of pulp on the genre and the game, especially in the gritty aspects of sword and sorcery, as well as the Lovecraftian influences, but LotR mostly ignored the pulp and crafted something new. And, in my opinion, there has always been just a touch more of Gandalf and Bilbo in the game than Conan or the Grey Mouser.