If they had two parallel flywheels that could be accelerated separately, I think that gives you rotation around an axis perpendicular to whatever surface the cube is resting on. It appears from the video that they have just a single flywheel, so maybe they're just taking advantage of how "noisy" the system is. That is, if a cube probably lands a bit "off", the next instruction can either fix that "error" or exaggerate it. Of course, they might also be just arranging everything carefully by hand before they start the camera. They never claimed the system was finished.

Cubes are easier to think about, but they're not the only polyhedrons that fill space. I wonder what this would look like with truncated octahedrons?

Presumably the flywheel axis can be rotated internally.

From the one look of the internals (1:50 in the video), there does not appear to be room to rotate the flywheel axis. That said, I would expect that is where they're headed when they can figure out how to use some of the space more efficiently.

You could have three sets of contra-rotating flywheels, which would give you much finer grain control of the motion.

I thought about this possibility, but having 3 flywheels increases the weight, which decreases the maximum angular momentum / weight that could be applied around a given axis. This is, I believe, the relevant quantity if you want to know how far a cube could jump in a different direction.

If the flywheel could rotate on two axes (and spin on the third, presumably), you would still have full control on which direction you apply forces.

I think it can rotate only around single axis, other blocks can rotate axis of that block if they themselves can rotate around different axes.