The word 司机 is formed by directly combining two meaningful characters: 司, which means "to manage" or "to take charge of", and 机, which here means "machine" or "mechanism". It is a straightforward conceptual compound, where the first character describes the action and the second specifies the object of that action, creating the literal idea of "one who manages/operates a machine", which semantically narrowed to specifically refer to the operator of a vehicle, a driver.