A high contrast screen is virtually doing the exact same thing as a ND (neutral density) filter placed over the projector lens or in the case of photography a camera lens. An ND-2 filter is commonly used with projectors to attenuate the projectors output by 50%. In the case of a ND-2 screen it will also attenuate 50% of the light reflecting from the screen. No one questions using a ND filter in photography as weakening the cameras ability to reproduce white in a photo they just know that it changes the exposure iris by one click. Putting one on a projector doesn't change the spectrum of light making whites gray in any way. It only is limiting the intensity of the total light output. The same is true with doing such at the screen. The only difference is at the screen the ND surface is also acting on all stray light striking the screen attenuating it at the same ratio. Of course the drawback is if you have two screens of the same rate of dispersion one being a 1.0 reference white and the other acting as a ND-2 to get the same brightness of image output the later projector would have to be outputting twice the lumens. The reward being the screen could tolerate more light coming from the room.
That's the effect neglecting the idea of perception of contrast. In a brighter environment our eyes iris reduce allowing the brain to see the best CR possible and the screen shade becomes reference black and the contrast extends to the brightest area being reference white. This is easy to test at home by watching the credits at the end of a movie white letters on a field of black. Examine the black closest to the white and the black at the edge of the screen they are both the same black but the closer to the white you get the better the black. This is also the same black you have been watching during the movie but in the movie the image was overall much brighter increasing the perceived black.
Most high contrast screens don't stop at just being darker and attenuating light though they then add in elements of directional gain that focus more light to the center seat and less to the far side seating. This gain can bring back some of the lost brightness along with rejecting ambient light coming from the sides. Directional gain is not without issues though. Those being, it starts to exaggerate any tendencies to warm or hot spot the center of the screen. The high contrast screens are carefully designed to take things as far as they can in improving the screens ability to work in less than perfect conditions and having an outcome that given all the variables is a net win.
Below is a photo of an experiment I did with a homemade screen that was as black as coal. The lumens were increased by using a bright projector and a very small screen. The objective of the test was to show white along with black and all colors could be projected off a very black screen. This photo was taken with an ambient light level brighter than most office settings.