It is precaulculated global illumination using the static world model. The moving objects are not in the calculations. However, it does a lot to improve the perceived genuineness of the scene.
Mirror's Edge was not the first game using this. Max Payne (the first game) used radiosity on finite elements to calculate global illumination in the static world models. You can see it in many places, color light bleed for example. This is the first game I know about that used global illumination color maps. Maybe there are earlier games.
Some game might have used radiosity on their shadow maps, but these were often monochrome back in the days.
Now we are starting to see dynamically calculated global illumination. Quantum Break was one of the earliest game having real-time global
illumination. That's why the game sometimes has a grainy appearance as some shortcuts must be made.