Interesting note: There are at least three different kinds of 'shaky/vibrating' notes in my song:
First there's the standard, Vibrato.
Second there's the less-used alternative, Tremolo.
And finally, there's something which, in this form, is unique to chiptunes: Arpeggiation.
While the humble arpeggio has been around since pre-medieval music as a way of simulating chords, the high frequency at which they can be played by electronic devices causes them to create unique textures. Unfortunately, this powerful sound can quickly flood the texture of the music, so it has to be used carefully. Since I like my music fairly busy, I was ok with using lots of them along with all the other sounds, but you'll notice that the song you linked to keeps it far simpler to avoid it becoming overpowering.