MIDI, for sure. This controller is a USB slave device, which means that it needs to be plugged into a USB host device for the USB port to work. Now, making a USB host device on an Arduino is a big project, whereas a MIDI receiver is quite straightforward. IIRC, it's just a 5-pin DIN socket, an optocoupler and a few resistors. The Arduino's serial port can be set to the MIDI baud rate with just:
An optocoupler is sometimes called an optoisolator; it's just an LED and a phototransistor in an opaque package, usually 6-pin. There's a ready-made MIDI shield available, too.