The brake is an internal force though (the force and its reaction both act on the bicycle). The whole unit's only external forces are from the fans so that's all it can use to translate. That and bumping into things.
Come to think of it - in air you're constantly bumping into things - air molecules. I think it could technically be possible to steer in zero-g within an atmosphere by pure rotation (e.g. consider that a fast-spinning object is kind of a (crappy) fan).
It uses an array of 12 small rotating fans placed around its surface to push jets of air and move itself from place to place.
My point was that in principle, you could abuse reaction wheels to give you translation capability if you're moving through air.