the picture doesn't show it very well. you set the hinge on the rear of the box (I'd use files to turn it into a butterfly hinge for prettiness) so when the box is closed the hinge is in the 180 degree position, when the box is opened the hinge opens to 270 degrees, thus you get 90 degrees of movement. you have to notch the lid and the box in order for the barrel of the hinge to sit inside of the box frame and I'd be tempted remove material so the hinge sits flush with the box and lid walls for neatness.
so in that picture those 2 pieces represent the back panel only, think about it, how would that hinge pass beyond 180 degrees? the wood is in the way.