Technically, no additional energy is wasted using this concept than with any other windmill concept. That is if everything is perfect in both cases there is no additional energy loss. First, this dome-windmill will be very sturdy. But, it will also require a high start-up wind speed. Once is gets turning, it will probably wobble from imperfections in the dome build and wind forces hitting parts other than the blades. This can be compensated by building a trackway for the rim to run in; however, this means friction losses.
Another problem will be the reason windmills are designed the way they are. The wind stream is disrupted close to ground level by trees, hills, etc. To get around this, the actual windmill is placed 50-100 ft above the surrounding landscape. In order to reach this strong wind, a very large dome would be required; say 50-100 ft radius. A lot of energy would be wasted in turning this entire structure.
However, there is one situation where this dome-windmill would be very useful. The winds accompanying the pole shift. Build the dome very large and extra sturdy, and build it in land as clear and flat as possible. Set it so that the produced energy is used to electrolyze water and compress, or liquefy, the resulting hydrogen and oxygen. The oxygen can either be used in a sealed dome's atmosphere, or can simply be vented off.
One other side note, this dome-windmill won't be quite that inexpensive.
Offered by Jeremiah.