Arne,
Given that we may have some difficulty convincing David to dissect his new motor, I'll take my best guess. 100A actually seems pretty tame from what I was used to with model airplanes, where it was not unusual to pump 100A through a very small controller and a much smaller motor than what David has. Maybe an electrical engineer can step in with the details on mosfets, but my experience is that power mosfets are certainly capable of handling those currents. Also, remember, even at full RPM the mosfets aren't continuously on. I'm working from memory (thus there is good reason not to trust what I'm saying), but for example if you had a twelve pole motor you would switch the FET's 36 times in one full rotation. At part throttle the Mosfets are on even less of the time.
As for the motor, this could be done a couple of ways. First the wire can be smaller than you would use for continuous rating, because it is only energized part of the time. Also, you can do things like use two parrallel wires when a single large conductor would be unwieldy. I've seen motors for models where there were only two or three wraps of wire on a stator. It looks comical, but yeilds a very high KV motor (one that spins very fast at lower voltage).
So, my guess is that there is no voltage boosting taking place in the controller. Here's an example of a much tinier model airplane motor that could handle 2400 Watts @24V. This motor would have much better cooling, but it is tiny compared to what is likely inside the Haswing. The Haswing, really is just at the upper end of what would be used in large radio control models.