That sounds about right. Except I'd put Halo: CE for FPS.

Diablo II LoD----------------RPG
Starcraft-----------------------Strategy
The Legend of Zelda -----Action/Adventure/RPG (What ever category The Legend of Zelda falls in)
Red Faction-------------------FPS
Road Rash---------------------Racing
Kirby's Adventure---------Platformer
Super Smash Brothers---Fighting
Guitar Hero-------------------Music
Rampage-----------------------Killer Dinosaur Category

Seeing you said game and not series...

Super Mario Bros. - Platformers
Pokemon Red/Blue/Green - RPG
The Legend of Zelda - Action/Adventure
Starcraft - Real Time Strategy
Street Fighter 2 - Fighting
Halo: Combat Evolved - First Person Shooter
Gran Turismo - Racing
Metal Gear Solid - Stealth
Tomb Raider - Third Person Shooter
Resident Evil - Survival Horror

Yeah I think Tomb Raider would be a better choice than Gears of War for TPS.

I still think that Pokémon has done more for the RPG genre than Final Fantasy

Super Mario Bros Platformer
Final Fantasy 6 JRPG
The legend of Zelda Action Adventure
World of Warcraft MMO
Street fighter 2 Fighting
Guitar Hero Music
Wings 2 Aces High Flying

Super Mario Bros. - Platformer
Pokemon R/B/G - RPG
The Legend of Zelda - Action/adventure
WoW - MMO
Street Fighter 2 - fighting
Guitar Hero - Music
Ace Combat - Flying
Racing - Gran Turismo
FPS - Doom (Halo CE?)
TPS - Tomb Raider

final fantasy its huge everywhere else. DQ it's only huge in japan.

God of war : for hack and slash.

msg: stealth assasination.

LBP for online multiplayer platforming.

RPG: FFantasy.

FPS: call of duty.

TPS: Uncharted, it have a cover system a decent story, and even platforming and hand on hand fighting.

fighter: tekken.

the Legend of Zelda=action adventure
mario=platformer
CoD=fps
RE=horror
street fighter=fighting
gears of war=tps
FF=rpg

FPS: Doom and later Half-Life
Hack'n'Slash RPG: Diablo
RTS: Starcraft
Adventure: Zelda
Platformer: Super Mario Bros.
MMO: Everquest and later WoW made it mainstream