Balloon Fighting is a prominent game mode as well a popular sport within the Balloon Fight series.
In Vs. Balloon Fight & Balloon Fight (NES), the player is tasked with clearing a phase of all Balloon Birds on screen. To do this, the player must first pop their Balloons, then either tear their parachute or kick them when they're grounded. When all of them are defeated, the player moves on to the next phase.
According to the manual for Balloon Kid, Balloon Fighting is a popular sport in Pencilvania. Although the typical phase-clearing gameplay isn't present in this game, the manual is referring to the Versus Mode of the game, where Alice and Samm compete.