Do they own the rights for the movies, books or both? This is based on the books (so includes places excluded from the movies)...
Doesn't work like that. They all own the rights to the books (or at least some of the books). New Line Cinema owns the patents to make movies based on the Lord of the Rings and the Hobbit (but not any of the additional material). Decipher had separate contracts with Tolkien Estate and New Line to make the card game. Parker Brothers owns the right to make games based off of both as well (again, a dual contract). It's all very complex but basically Tolkien Estates and New Line Cinema gave out rights to a bunch of companies to make merchandise for the movie releases, but some of the companies kept their contracts long after the movies came out and still make stuff in relation to it. Like Star Wars, Indiana Jones, Harry Potter, and other franchises, it's all a complex network of patronage.