Here is my take on what game invented a genre. It isn't the earliest game of that style. Instead it is the first popular game of that style. Why? Because if the game isn't popular enough, then we don't even consider it a new genre. But if it is popular, then it inspires a bunch of imitators. For example, FPS games in the 90's were actually called "Doom clones". Doom is actually the game that created the FPS genre. It doesn't matter that Wolfenstein 3D came first. No one would be using FPS or "Doom clone" to name this genre if Wolfenstein 3D was the only example. And Katamari Damacy is a unique style of game, but no one has come along to call it a "sticky roller genre" or "growing collector genre", because the game hasn't inspired enough imitators. On the other hand Donkey Kong (1981) should be considered the first platformer. It doesn't matter that Space Panic came first. No one liked Space Panic (and it didn't even have a jump button), while Donkey Kong was one of the most popular arcade games and it definitely inspired a lot of other platformers that came after it.
So, the first game that is popular enough to inspire enough imitators to call it a genre, that is the game that I'd say invented the genre. Here are a few examples:
Pong clones - Pong
Shmup - Space Invaders
Maze Game - Pac-Man
2D Platformer - Donkey Kong
First Person RPG - Wizardry
Top Down RPG - Ultima
Adventure Game - Colossal Cave Adventure
Edutainment - Oregon Trail
Action Adventure - Adventure
Light Gun - Duck Hunt
Action RPG - The Legend of Zelda
JRPG - Dragon Quest
Fighting Game - Street Fighter II
Metroidvania - Metroid
FPS - Doom
Roguelike - Rogue
Racing - Rally X
3D Racing - Pole Position
