It's music created with sound chips from anything that synthesizes sound rather than playing back premade ones.
Today, most/all chiptunes are made through emulated sound chips and not physical ones though.
Basically it's music that you forge from scratch inside a computer. MIDI, meanwhile, uses samples made to sound like/recorded from real instruments.
In other words, making songs like the one I posted is a remarkable feat, much more technically difficult than stringing together a bunch of MIDI notes.