Ico

A boy born with horns is sealed inside an empty castle to die. He breaks free and finds Yorda, a pale girl who speaks a language he cannot read. The game is the two of them trying to get out together. You literally hold a button to hold her hand and pull her along, boosting her over gaps, fighting off shadow creatures that drag her into pits when you wander too far. It came out on PS2 in 2001 and almost nothing in it is explained. The bond between the two characters is the entire mechanic and the entire story.