It is hard to get good pictures of the rainscreen assembly, but here are a few courtesy of Mr. Canivet.
The point of the rainscreen is to allow air to circulate behind the siding and dry out the backside. This way the moisture doesn’t instead get sucked inwards into the insulation and stud bays and the paper-backed sheet rock when you turn on your industrial kitchen hood. This can cause all sorts of problems. It also just keeps the moisture from lurking behind the siding.
The siding is 5/8″ thick fibercement lap siding. the furring is 1.5″x5/16″ cedar strips, and the drainage plane is good old-fashioned 2-ply building paper. In order to keep insects from building nests behind the siding Guillaume came up with a simple detail using wire mesh and filter fabric at the top and bottom and above and below each window.