What does it mean for a thing to be “authentic”? Tolkien hasn’t created anything since he passed away. I hear they used computers to some extent when making the lord of the rings movies, something Tolkien certainly would not have done. Should we thus criticize the movies on the basis of their authenticity?

Again, I think you've misread the parent comment here. The Lord of the Rings--the actual books, the content of the work--is partially about authenticity, in the same way that Spiderman is about power and responsibility.

I'm not talking about the provenance of the work, but the content of it.