Well, I think your mind may be a bit set already! I agree that on the surface, you have a justifiable argument that the old man was, indeed, defeated. But it depends on the criteria you use to define victory.
The victory for the old man comes not in winning the fight, but being willing to accept the challenge. This man had gone eighty-four days with nothing, no luck at all. And his reputation was as a master fisherman. Yet he kept on going out there, day after day, to try to restore his pride.
Keep in mind, also, that the old man is a classic Christ-figure. He has one disciple and is skilled at a humble profession. The sea becomes a wilderness for him, a place where he is tested. He goes through physical suffering, including the mutilation of his hands. The whole episode with the great marlin lasts three days. His return with the carcass is like a resurrection, and when he carries his mast up the hill to his shack, he looks like a man carrying a cross. When the people see him, they begin to have faith in him again.
I would say that's far from a defeat, wouldn't you?