It’s not actually The Lord of the Ring at all. The Lord of the Ring took place in the 3rd age of Middle Earth. This takes place in the 2nd age (mostly), several thousand years before TLOTR. It’s mostly based on Tolkein’s works in The Silmarillion. And yes, they have rights. The Tolkien estate has been cooperative and supportive (though I suspect $ signs are a big factor for that support).
You are correct. I’m glad you posted the facts because then I didn’t need to.