Building a story-centric first-person shooter, a competitive multiplayer RTS, or a fantasy MMO, puts you squarely in competition with the big guys, right where their massive production budget gives them an edge.
Even in those, you can still change the game. First Person Shooter was taken on by Portal, who made great use of an uncommon feature. even with these seemingly vague genre's you can still add entirely new concepts that can change the way the game is played.
for a first person shooter, you could go through a level, blasting your way through. Then, you replay the level as one of the enemies, and your old character will use an AI to try to follow the same path and deviate when needed. and you go back and forth as different characters in the same repeating world, constantly trying to best yourself. And the AI can also learn your repetitive habits, and apply them when it tries to mimic you.
Its a game play mechanic that is very different from most FPS's out there, that don't make sense to apply to the current main stream games without significantly messing up their stories.
Also, Clone Wars has the repeating first person shooter, which also works well, but is significantly different.
But I think your original point was that you shouldn't compete directly, and even those genre's allow indirect competition quite well.