I'm pretty sure Saul didn't own *all* rights, just exactly what it said in the article: merchandise, live events, certain film and TV rights for LOTR and the Hobbit, plus matching rights for The Silmarillion and other materials. The article specifically said that the Tolkien Estate retained rights for TV shows based on LOTR of 8 episodes or less, hence how Amazon was able to go directly to the Tolkien estate and secure the rights without cutting Saul in.
The Tolkien estate presumably retains theme park rights and would need to be negotiated with if we want to see Middle Earth in EU.