After defeating Wario he drops something and runs off, but I could never identify what he drops or figure out why he drops it.
According to Mario wiki, that's one of his shoes:
Mario was still able to defeat him in battle. As a result, Wario shrinks and begins crying in defeat, but then throws one of his shoes at Mario before making his escape from the castle, with Mario following suit.
And for the reason, as also said by @TripHound, that move is considered a Shoe Slap:
throwing shoes happen to be a common occurrence in some cultures and countries, with some seeing it as an act of disrespect.
After being defeated, Wario throws a shoe and flees the throne room.
This is easier to see when playing in color using Super Mario Land 2 DX: 6 Golden Coins
Screenshot from video by LETSPLAYmarkus