The naming conventions of MIDI take a little getting used to.
To send MIDI from Arduino you need a 5-pin MIDI OUT circuit (because the data is coming OUT of the Arduino). You then connect that to the MIDI IN on the USB adaptor (because you want the data to go IN to the computer). That's how it works.
How are you checking if it is working or not? If that code does anything it sends very short, fairly quiet notes.
Steve