I think the "magic" quality is not exclusive to nintendo but they have nailed that quality on the head so many times that most people associate them with "magic". I think the magic feel comes from games that have a high level quality but not only that but have ingenuity, uniqueness, newness...some examples are how nintendo has taken technologies and incorporated it in unique ways like the rumble Pak, joystick, wiimote, directional pad, dual screen.
also some revolutions introduced by nintendo in game design are mario 64(1st excellent 3d designed game), ocarina of time(1st time z-targeting created), super Mario bros (essientally the game that turned america on), mario Galaxy (antigravity), mario 3d world(the best interpretation of 2d-3d with multiplayer), etc...
this quality is not exclusive to nintendo and other games that have hit the nail on the head are street fighter 2, megaman, resident evil, devil may cry, etc but for some reason capcom (although had Magic before) is in deep financial woes.. Maybe they weren't innovative enough in game design and quality
