The line was clear enough to me. The book was rejected by a variety of publishers for a variety of reasons, not all of which have anything to do with the quality of the book. The book won an award because it was competing in a field of ... what, a dozen, a score? ... of other books and was judged by a handful of people to be the best of that litter. IOW, entirely different audience with entirely different criteria.
This happens all the time, in all fields of art. The movie that's panned by critics but loved by the audience; or, hated or ignored by everyone but goes on to become a cult hit. Bands that are loved by their fans but never get beyond that fan base. Authors who are declared "overlooked". It's a big world and there will be many different reactions to any given work of art, and those reactions will change over time.
The advice never to give up always comes from someone who made it. I'd argue there's definitely a time to give up, or at least to get on to other things. If it's with trad publishing, the time to move on would be when your agent says they've tried everything, knocked on every door, and every publisher has declined. What would not giving up even mean at that point? Save, of course, going self-pub. (here, self-pub would mean getting oneself down to the pub)
My advice to Mr Napper would be to redefine success. Getting the book done is success. Getting an agent to take it on would be a second success. Getting a publisher would be third. Awards would be another. Selling N copies would be yet another. There are opportunities for success everywhere! They all are contingent upon that first one, though.
And even there, I'd say, give up if you can. If it's possible for me to give up on a story--that is, not to finish it--then that wasn't my story. I've had a couple of those. They sit even now in the corner, like outgrown toys. But because I "gave up" on them, I wrote other stories. So there's that.