We could say "tragedy," but that would be misleading. Actually, it would be wrong, as far as we’re concerned. The ending isn’t really tragic (do you see a death or death wish here?), and there’s a reason this book doesn’t follow Booker’s tragedy plot: it’s not a tragedy. Tell that to the neighbors. Or write us an essay arguing that it is a tragedy.
As for the "quest" bit, we hesitated here, but then we were feeling bold so we decided to just go for it. The old man is questing to catch a fish, there are lots of obstacles in the way (the aching, excessive pain, excess), and we learn about the protagonist as he struggles to complete his goal.