He eats. And bathes. And poops. We just don't see it/it's off-screen because we don't need to. It's one of those Law of Conservation of Detail things - if a person isn't important to the story, they usually aren't named or given a backstory, if it is not important to the overall story for the character to eat, we don't see that - it would put a damper on the game if you had to get Link fed every so often or he'd get weaker. It would be an interesting addition to a game - at first, but then it would just get annoying.
Besides, in A Link to the Past, you can ram into trees with the pegasus boots and get apples that restore your hearts. I assume he's eating them.
When I write a story, I'll have the characters eat and such, but only if it's important for some reason - or a break is needed in the action. I *will* have them take care of their horse if they have a horse, because the "automaton horses" trope bothers me as someone who takes care of the beasts in real life. I don't really *need* to detail my characters' water closet activities because that just strikes the reader as crude.