The word "paintball" refers to a game where players shoot small balls filled with paint at each other using special guns. The idea is to mark opponents with paint to determine the winner.
The cover mechanics translated brilliantly to online, the focus on giving your team - mates covering fire, open arena - like maps and flanking opponents making Gears feel like a brutal game of paintball in terms of tactics, particularly compared to the popular corridors - and - corners first - person shooters of the time. (gamestm.co.uk)
The title refers to the name of a game played out on Jonathan's college campus, whereby participants stroll around with paintball guns in an elimination game of sorts. (qwipster.net)
In the first Disney Infinity, you couldn't make, say, Jack Sparrow run around Monsters University and pelt people with paintball guns. (gamesradar.com)