Why does bandit work on gangplank

Cause he's a pirate.

His Q applies on-hit effects as a melee autoattack. As such, he gets the 10 bonus gold whenever he Qs an enemy champion while Bandit is available.

His "Q" counts as a melee basic attack, not a ranged basic attack. Bandit gives 10 Gold on melee attacks and 3 Gold for ranged, so GP gets the full 10 Gold when he "Q"s you.

I had actually not considered that.

I learned something! I may shut down for the remainder of the day.

Basically the idea is that it's not efficient to Q minions unless you're going to miss the last hit otherwise, so you want to use it to harass until you have trinity force and can one shot with barrels. So since Q acts as an auto attack you get 10 free gold on cooldown when you harass your lane opponent. GP is a champion that needs a ton of money to get through his items, so the bonus off of bandit helps him get up there.