It doesn't work by itself with the heat source higher than the floor you want to heat; that's why the diagram has a separate pumped loop for floor heating. As long as the pump works, this setup should work well
enough. The caveat is that you are not going to get more than a small fraction of your stove's output into the water. Most of it will radiate off the stove's surface, and what goes up the chimney is needed to some extent to maintain the draft so you don't get smokeback, and keep the exhaust hot enough to not form creosote in the chimney. Personally, I don't think this kind of arrangement with a woodstove is likely to deliver enough heat to the floor to be worth the effort. If you do draw enough heat out of the exhaust, it will cool it enough that creosote is a serious danger.
If you want to get hot water from a woodstove, I would recommend wrapping collector tubing around the stove itself, not touching the stove surfaces. The larger the tubing, the safer it is likely to be, as larger volumes of water are harder to flash into steam and explode, and larger tubing lets steam bubbles escape to the open tank easier. You do want the collector tubing to have a constant upward slope so that heated water has a good path to rise to the tank.