The adventure is the skeleton of Zelda, where the player goes, what they discover, what they find, what they see. The string of events the player discovers (actually they are being led on a very carefully designed path) is the skeleton of Zelda, the arcade gameplay is the skin that encompasses it, keeping the player entertained from event to event, from discovery to discovery, staving off disinterest until the next wonder is uncovered.
The reason Zelda seems non linear is because of all the effort put into disguising it. Zelda is like a maze, there is a huge world with only one path to navigate it, full of dead ends. Only one path. But dead ends are boring. So they filled them with zany characters, fun things to do, secret items like a cape, or wand, heart peices, a cursed fairy that upgrades your items, a character in need of your help who will help you in return. The player is overwhelmed with content, and thus cannot distinguish the one true path among all the wondrous dead ends, all the optional dead ends that are not requirements to beating the game. But its there, its always there, the dead ends are optional, but the player must travel the true path to make progress in the game
