No, it does not support selective occlusion. Much like Google Glass it's a microprojector against your face, albeit this is two-eyed whereas Google's has one.

The glasses are not a normal display. Most displays are opaque, and can display pure black by simply not emitting any light. These glasses are transparent, so when they don't emit any light you see whatever's behind the display, not black. Displaying true black on a transparent display requires an extra element which can selectively block incoming light. These glasses don't have such an element, and cannot display black or dark colors unless you happen to be looking at a black object in the real world.

Virtual objects occluding real objects is in fact nearly impossible. The way you're thinking about it with the extra LCD layer isn't actually a viable solution for this sort of display (or any sort of display my mind can come up with right now). The way glasses such as these work is a lcd screen hidden in the side of the glasses is viewed through a beamsplitter that combines the image of the screen with the real world. The screen appears to be "at infinity" from the viewers perspective. Unfortunately to do occlusion on glasses like this the light would have to be blocked between the source of the light (outside world) and the viewers eyes. The light blocking layer would always appear blurry from the users perspective since it would be so close to the eyes. You would also have problems aligning the light blocking layer with the screen as the apparent position of the screen in the glasses is dependent on the position of the glasses on your head.