Oh boy, a licensed property, so early on?! At least it's not a video game based on a movie at this point, but it is based on the book, or rather sits alongside the events of the book - so much so that it was sold alongside a copy of the Hobbit, which makes The Hobbit some kind of collectors edition waaay before such a concept would dominate the gaming market. And there wasn't a standard edition, it was straight up cross-media promotion, and it was everywhere. Name the home console of the 80s and The Hobbit seems to have been on it, so it must have been good...
Luckily for me, it's available on the Internet Archive. Doesn't come with the book though, but I'll let that slide.