Not an EE here, but I've dragged some circuits together as a hobby and have only used I2C. Why would Nintendo opt for I2C instead of a differential pair? Is there some extra part cost? What part(s) would you use to go from I2C to differential?
I don't know why Nintendo did it. But it's certainly quite convenient, there are even standard form factor breakouts for the Nunchuck like in the link below. This gets you a controller with accelerometer, 2 buttons and a 2 axis joystick with plenty of libraries available for using it with Arduino, RPi etc.
I don't know about I2C specifically, but a related device is a serdes (serial-deseria) which converts between a parallel interface and one or more differential pairs.