I think the big problem for electrodacus is that at wind speed (and faster) there seems to be no relative wind to power anything. The only way to go faster than what's pushing is via some stored energy, ergo there must be some stored energy somewhere. Where? The only possible place, given that the prop is quite important, is the prop wash.
Which seems reasonable if you haven't seen this thing work, and all the explanations so far seem to run up against the problem that at wind speed there is no push (or even pull), so there is no obvious way this could be working.
So... how about an alternative explanation without the maths that no-one can agree on...
ISTM the most important thing to bear in mind is the prop is rotating and pushing air back. For a given rotational speed, the air will flow backwards at some derived speed - the faster the prop goes the faster the air flows back. You could use this to push the vehicle at a given speed by altering the speed of the prop, so we could say that the prop turning at xrpm is equivalent to airflow of ym/s. It works in reverse, of course - push the vehicle and the airflow will cause the prop to turn proportionally to the vehicle speed through the air.
So, back to wind speed and no push. But there is a push - the prop wash is effectively a wall (albeit quite flimsy!) moving at a negative speed relative to the vehicle and tied to the vehicle. If the vehicle is moving at wind speed, the prop wash is moving backwards at some speed relative to the vehicle and thus the wind. The wind can push against the prop wash to continue pushing the vehicle a little faster. In effect, the prop wash is an infinite length of the string we see with that yo-yo.
By what powers the prop? It is still the wind because it is able to be pushing the vehicle still. With the prop wash moving backwards and effectively part of the vehicle, the vehicle is not at maximum speed relative to the wind, so the wind can keep pushing it.