Thst being said, WB doesn't seem to be involved so obviously they impressed the Tolkien estate?
It's actually even a little bit more complicated than that... This one is truly wild.
Tolkien sold the rights to film, play, and merchandise to United Artists sometime around 1970. UA ended up selling the rights to another smaller film company owned by Saul Zaentz. Zaentz wasn't a filmmaker originally. Zaentz's actually owned a small record label that signed Creedence Clearwater Revival. CCR was a huge success for Zaentz and he used the profits from the records to found his own film company and later purchase the rights to LOTR.
As a side note, CCR and Zaentz's label actually got into several legal battles accusing Zaentz's of litany of things. John Foggerty actually sued the label in a case that went before the Supreme Court. Foggerty won. Foggerty's song "Mr. Greed" is about Zaentz.
Zaent's film comp produced several films including the movie adaptation of "One Flew Over the Cuckoo's Nest". This film company started a division called Tolkien Enterprises and are responsible for the majority of LOTR related works we see today. Miramax actually licensed LOTR from Tolkien Enterprises/Zaentz to make the movies in the early 00s. The company later rebranded as Middle Earth Enterprises.
Middle Earth Enterprises is the company that licensed the game rights to WB. As far as I know the details of the licensing agreement are not public and it is not an exclusive licensing deal. WB has another game in development and Middle Earth Enterprises has also licensed the rights to Daedelic for this title and Amazon games for the upcoming MMO title.
The Tolkien estate was actually in a legal battle with Middle Earth Enterprises at one point because they contended that Middle Earth's merchandising rights only pertained to physical goods-not video games and certainly not new narrative content. They ended up settling out of court.
Not complicated enough? The rights to the upcoming Amazon TV show were licensed by the Tolkien estate. Middle Earth Enterprises only owns the rights to The Hobbit and The Lord of the Rings film, plays, and merchandise; the rights to the Silmarillion and everything else remain with the Tolkien Estate. So Amazon has simultaneously licensed LOTR material from both the Tolkien Estate and Middle Earth Enterprises.
Another interesting note-Christopher Tolkien, J.R.R. Tolkien's son and the head of the Tolkien Estate was very much against the movies and other licensed products. He actually resigned just days after it was announced that Amazon would be making a series based on the Second Age. It seems like the rest of the family is not as protective of LOTR and is actively considering licensing deals.