Probably should ask this in the powerlifting forum. It more closely resembles a powerlifting (half) squat. As mentioned above, the box takes away the stretch reflex b/c you're supposed to pause briefly on the box, and then explode off it w/ your glutes/hips/hams. Works good for the powerlifting squat and the deadlift.
Long story short, just another squat variation, but aimed at improving the powerlifts.