Looks really nice. I wish you the best with it - however, I think your design will (at best) be less efficient, and (at worst) result in a shortened lifespan for you chest freezer.
Traditional fridges/freezers have a compact condenser coil with a fan to shed the heat. Modern chest freezer design did away with the condenser coil, and instead has a network of high pressure tubing in the side walls that is in contact with the outside skin of the freezer. It uses the outside skin to radiate and shed the heat from compressing the freon. There are no high pressure tubes to shed heat from the bottom. The compressor does generate a little heat, and does need to be vented - but not nearly as much as the skin.
Wood is a great insulator. By boxing in the 2/3s of all the walls (back is open), you have significantly reduced it's capability to shed heat. The unit is designed so that by the time the high pressure gas gets to the inside coils, the freon has condensed to liquid. It then goes through a tiny opening, into the much larger return lines. The pressure drop results in cooling. In your case, there will be much less liquid at that transition point - and much less cooling capacity. Your compressor will run more frequently - even at "fridge" temps.
Other wood clad keezer designs I have seen have incorporated a fan to blow air between the wood and the skin of the freezer. The best designs ensure that the air circulates completely around the unit. You might want to consider retrofitting something like that in your build. Otherwise, my money is on that unit crapping out in 2 yrs or less.