There is probably multiple ways to achieve this, and I am making some assumptions, but here is what they appear to be doing.
1) Rasters on top of the basemap, but under a transparent dark rectangle to dull colors. Vector boundary layer for all Management Units on top of the transparent rectangle. They also appear to have features for each "outside" area for each Management Unit. These vector layers have the same dark transparency applied to fill, and the larger rectangle has holes cut into it matching these boundaries.
3) When user turns on a Management Unit, it is doing so in a List widget that uses message actions to make a selection on the chosen Management Unit and also filters the dark transparent overlay areas to create a hole over the chosen unit making the colors more vivid.
As far as the widget configuration, it looks like they have a List widget (with png images for each Management Unit) grouped with a Layer list widget (toggle for Containment) inside the main Widget Controller set to expand all on opening.
