I agree with @ShintaiDK and disagree with @RussianSensation.
Making the game run on a Pentium should be fairly easy given that games like Ryse,AC:Syndicate,etc worked on a Pentium(source:I played those games on my Pentium G630).So what reason could Mirror's Edge's developers have that the game cannot run on dual cores but other more demanding games can run? Like Shintai said i'm sure its just a 0+1 core lockout that could be easily be disabled by them allowing it to run on Pentiums.
If you're a developer, you want to deliver a certain standard of experience on whatever platform you're developing for.
While I'm sure a dual core could work with Mirror's Edge, I also believe that the gaming experience would be very subpar compared to a quad core or greater CPU..
With a dual core, you could look forward to much longer loading times, streaming problems, stuttering, hitching and God knows what else..
Case in point.
That link is from PCgameshardware.de's review of The Division. They tested it with a simulated dual core processor with HT. They found that the load times increased dramatically with a dual core CPU (several minutes long), and there were all sorts of ugly streaming issues like running into invisible walls and barriers because the streaming was so slow..
Using Google translate:
users of older and frail processors from Schlage Core i3 must be prepared for moderate to severe problems in The Division. With four CPU threads the game logs when starting the shortfall of its minimum requirements, then runs but more or less - as long as you can tolerate minutes long load times and smooth liges streaming. With only two cores / threads the Open Beta launched not only - the final version already, as we discovered surprised at posttest. What we saw then, is unprecedented. Expected we have endless loading times and low frame rates. The what we got, but with a curious Extra: When we wiggled our way through the first measurement, ran our alter ego in an invisible wall (see picture). A real showstopper - the game with two cores in a unique way unplayable.
So with this in mind, it's not surprising why DICE or any other developer would not want to risk having their customers try to run the game on a dual core CPU.
It's not because they can't do it, it's because they want to deliver a good experience; something which a dual core is unable to do.
So just because you can do something, doesn't mean you should do it. I can walk all the way to Toronto, but flying is a helluva lot easier and faster..