Bioshock? Half-Life? Fallout? The list goes on...
Yes. To all. Yes, I have played them. No, I didn't like them. They didn't suit my tastes. Bioshock was... an immersive experience, but one that failed to captivate me. Half Life was cut scene that I could walk around in at first, then it just lead me down a somewhat linear path to shoot things. Fallout was just too much landscape for me. And the slow motion shooting just didn't keep my attention for very long... despite the tactical reasoning behind it.
You know which 'traditional' shooter I liked? The first Left 4 Dead. I had fun with that one. And I actually hate zombie-themed games and movies. But it didn't matter, because I could just pick up and play it. That, and it reminded me of the good old days of RE2. It's not quite as good as RE2, but it stands on it's own. I never plated the L4D sequels, though...
Mirror's Edge certainly isn't an FPS. It's first-person platformer. Don't lump my traceur exploits in with Sergeant Shootypants McDuty :/
You can't stand up against a whole tyrannical regime with kung fu antics alone (as much as I would love to... even in first-person) You need some sort of range-based power. Even if it's fireballs from your hand like in ''Magic Carpet''... which could technically be listed as a flight-simulator by that logic.
Not that I disagree outright, but I'll explain myself in a moment.
I know you can play the entire game by not firing a shot, but if you tried that even in a semi-realistic scenario, you'd be swiss cheese before completing the first wall run... or tic-tac-toe, or whatever traceurs want to call it.
It's even difficult to do so in Hard Mode (yes, I know that's the point, but do you see what I'm getting at, here?)
I'm not saying you're wrong, I actually agree with you. I like the fact that it's not really an FPS. But you can't deny that it has shooting in it. It's the same thing with Metroid Prime. It's not a shooter, it's a first-person adventure. With shooting used as a means of defense. Same thing with Condemned. It's first person melee-horror. With shooting.
Besides, Mirror's Edge is ''realistic fantasy''. Part of that fantasy is diving off the side of a building while shooting at the bad guys... something that could only be done in Max Payne... which, unfortunately, was pure shooter.
The only way to remove the shooting element entirely would be to give Faith extra gadgets, Dishonored-style... and that would only serve to take the player out of the experience.
Or this:
http://www.cracked.com/blog/7-real-suits-that-will-soon-make-world-cooler-place/
So, in conclusion, no it's not a shooter -- but yes, unfortunately, shooting must be a part of it to complete the illusion.