It's interesting to think about what 'creating a genre' means. A game might not be the first to introduce certain gameplay elements, but could have popularized it, therefore became genre defining.

Examples:
Platform fighters - Smash Bros
Platformers - Super Mario Bros
Action adventures - Zelda
Metroidvania - Metroid/Symphony of the Night
Fighters - Streetfighter2
RTS - Warcraft2
Simulation - Sims
etc.

I have only played SFIII Episode I, are episodes II and III available in English.  

Homeworld

Full 3D Space Strategy. I can't think of anything similar before it.

I think there are fan translations out there

I need to check that out.  SF is one of my alltime favorite series.  Back on the genesis was I blown away.  

Could Pirates! be defined as beginner of some genre? Elite was the first freelancer game, but it's still pretty different.
What about SimCity? What city builders existed before that?
Do we count Breakout separate genre from Pong?
And I don't think anyone has said Tetris.

I think this is a more fun take to discuss but it is very different from the question asked. 

The first game in a genre often is not found being part of that genre until a game comes that popularizes it. What seem to define anything as its own gerne seem to be when a popular game gets copy-cats. A game that set the standard with most of the defining characters going forward for the genre is what I think of when talking about the first of its kind. 

Several genres are also such broad groupings while other gernes are more specific in what the criteria are. Every FPS for example looks to me very similar but since there are so many games in the genre I'm probably just ignorant and there are several different sub-genres worthy of its own name. 

Except I've named more games than anyone else.

If Wolfenstein 3D was the only FPS game, then there would never be a FPS genre.  It was not good enough to inspire imitators.  Once Doom came along, then there were a ton of imitators.  Doom is the game that actually made this style of game a genre.  The imitators are what turn a unique type of game into a whole genre.

Naming more wrong answers means nothing. Wolfenstien wasn't the first either.

Maze War comes from the 1970s. Same with Spasim. Midi Maze on Atari ST. Hovertank from Id Software even predates Wolfen 3D. The name escapes me atm but NES had one. There is a reason we have the words first and popularize. Nintendo did not invent Analog sticks either but they popularized them. Apple did not invent MP3 players but they popularized them.

The games come first, then we invent words to describe the genre when there are enough games of that type.  Pong was not the first table tennis game, but none of us would be playing video games if it weren't for Pong.  The games that first popularize a genre really matter more than the game that was technically the first but was a bad game.