However, adding a third polarizer does not help. At best, the same amount of light is blocked as with two polarizers perpendicular to each other. At worst, it allows more light to go through than two polarizers.
Whatever extra layer they're using, it's not a polarizer, so it can't be an LCD. It's probably some sort of electrochromic glass whose reflectivity (and thus opacity) can be controlled electrically. And they've figured out a way to divide the effect into zones which coincide with the pixels or groupings of pixels on the LCD. It probably doesn't have as much fine granularity of partial opacity as an LCD does (else they could just use it instead of LCDs since LCDs always block at least 50% of the backlight), LCDs have gotten good enough to where we can use them to generate 1024 shades (10-bit, though most panels are still 8-bit or 6-bit), while last I heard electrochromic glass was binary.