CNC Furniture has been for a few years already but hasn't really taken off. I believe this is because designers haven't spend enough time designing with that technology in mind. Most of the CNC furniture I found online have the typical joinery exposed or have a rigid feel. I played around with the ShopBot Buddy (worktable 4' x 2') and made a family of chairs: Lounge Chair, a Stool and this Dining Chair. I wanted to design a modern chair that would have a retro look, similar to a school chair but making it more ergonomic and comfortable.
CNC Routers have become affordable in the last couple of years and there are quite a lot of DIY CNC Routers out there. If you have a TechShop close by you can probably make it over there.
IMPORTANT: measure the thickness of your plywood! I purchased the white melamine plywood in 0.75” thick (19.05 mm) but as you can see from the photo, the it was 19.81 mm and the pre-finished walnut was 18.95 mm thick. This is really important to take note because the design has locking parts and we need to accommodate for a thicker material.