If you look at the picture of the inside of the firebox it looks like there could be a separate chamber at the top of the firebox where the stack connects. It is unorthodox, but may actually work.
Looking closely at the pics from inside and outside of the fire box it would seem that the stack is not tied into the firebox. There is maybe a 4" void from where the inside of the firebox to the top of the outside. I would guess that it does work but with a rather unusual design.
I'm now wondering if this is a great idea, proximity to the firebox may heat the exhaust on exit and result in more draw. Also curious at the metal thickness... if it's 1/4" the price is more than right.
The design is different, but I see no reason why it could not work. The thing that would put me off is it has only done two smokes and now he's selling it for the price of an OC Brazos. It is possible that he just built it for fun or as research into whether he wanted to fabricate as a business, but still... one wonders.
I can't see an efficient design there at all! If it is actually reverse flow, the smoke and heat would have to travel back downward to exit through the exhaust, and that is assuming that there is a plate that will initially force all of the heat and smoke directly into the cook chamber. My guess is this guy is not a Brethren and didn't run this design by a Brethren before he built.