The Were-worms of the East are only briefly mentioned in the book The Hobbit as a legend or folktale. They never actually appear in any of the books and Tolkien never described them. Also, remember that the Lord of the Rings movies were made years before Jackson made the Hobbit movies. If you look closely, you'll see other differences between the two trilogies such as Bilbo's map of Lonely Mountain is different in the original trilogy than how it appears in the Hobbit films.
"Tell me what you want done, and I will try it, if I have to walk from here to the East of East and fight the wild Were-worms in the Last Desert." - The Hobbit, "An Unexpected Party"