Yujiro spent his whole life being undefeatable when all he wanted was a challenge. To the strongest man in the world, no fight can truly challenge him. It's like an endless cycle: he's the Ogre, the strongest, and his pride and self-image can't let himself slack off on that - at the same time, it means that fighting, the thing he lives for, lost all meaning.
But to a man who's dedicated his whole life to fighting, anything but fighting can be a challenge - even something as simple as preparing a meal for his son. Baki may not have defeated Yujiro, the Strongest Living Creature, but he defeated the image of "Yujiro, the Strongest Living Creature" in his father's mind that had kept him locked in the cycle. He humbled Yujiro by sneaking a challenge he knew Yujirou could never win in right under his nose.
Losing is something people are scared of. But for Yujiro, losing has set him free. He no longer has to only be "Yujiro, the Strongest Living Creature." He can be "Yujiro, the Strongest Living Creature" who you never bet against in a fight, plus "Yujiro, the Piss Poor Cook" and "Yujiro, Working on Being a Better Father." I don't think that's a half-bad deal, or a half-bad way to end a series that's so manly in every way.