No, it really is possible to violate momentum conservation in suitably curved spacetimes. But this is a straightforward consequence of the laws of physics, not a "defiance" of them: it falls right out of general relativity. We still have a conservation law for the stress energy tensor, given by ∇_{μ}T^{μν}=0, it just doesn't give rise to separate global conservation laws on each component.

The same applies to the system they actually built, except that the nonconserved "momentum" is not the same as the usual notion. It's the conjugate momentum(https://en.wikipedia.org/wiki/Canonical_coordinates) for the coordinates on the surface.

It does seem that friction in the bearing and tension of the wires is not sufficiently controlled for the physical demonstration to be convincing.

However, the mathematics of it seems to have already been confirmed by a previous paper and the actual idea of changing orientation without exchanging momentum with anything is not novel.

You can turn a satellite by spinning up a flywheel and then reabsorbing the angular momentum when you reach the desired orientation.