Christian theology is that the entire bible is the word of God. So god is the true author of all books of the bible including Job. They claim the human authors received a revelation from the almighty and that this is how the book of Job came into being. So to a Christian the author would have to believe in God since God spoke to them and caused them to write this book.

So the author of Job was a believer, yet he didn't need faith to believe since he has a personal revelation. So if Christian theology is to be consistent with itself, he was a believer without faith so he was unsaved, therefore going to Hell.