Updated:
Taking the history
tag into account, I thought the games might be organized by decade of release.
1st:
1970s
BRICK: breakout(1976)
INVADE: space invaders(1978)
2nd:
1980s
GHOST: pac-man(1980)
BARREL: donkey kong(1981)
TRAFFIC: frogger (1981)
3rd:
1990s
DEMON: doom (1993)
EMPIRES: age of empires (1997)
MORTAL: mortal kombat(1992)
DANCE: ddr (1998)
4th:
2000s
CAKE: portal(2007)
WARTHOG: halo(2001)
GUITAR: guitar hero (2005)
WORLD: world of warcraft (2004)
Unknown
FOUR: ??? (19__)
TENNIS: ??? (19__)
GOLD: ??? (19__)
Original:
Here's a try, with some certain to be wrong:
One group:
Objectives: Cake (Portal), Gold (many many games), Brick (Breakout), Four in a row (Connect Four)
Second group:
Things to be avoided: Ghost (Pacman), Barrel (Donkey Kong), Traffic (Frogger), Demon (???)
Third group:
Games with two-player competition mode: Dance Dance Revolution/Guitar Hero/Tennis (Wii sports)/Mortal Kombat
Fourth group:
Key word is last in a multi-word title:DCS: A-10C Warthog/Age of Empires/Super Mario World/Space Invaders