If you don't want to know the campaign ending do not read further.
The first time I played the campaign I did not rip up the ring. I wasn't sure of that interpretation of the ending. It says "destroy" the card. Destroy is a game term that means send to the discard pile. Nowhere did I find instruction to literally tear up a card. However in that sentence the phrase "One Ring card" made it sound like it was out side of the normal gameplay.
I'm about to start a campaign with my wife, and if the the card must die to win then I want us to play it right. Besides it would be cool if she ended as first player and had to make the decision. So if anyone knows an official answer to "do we physically destroy the card?" I would like to hear it.