Hmm, a gyroscope, a music player and a flashlight. Sounds like an idea for an iPhone 4 app!

Seriously though, in the video he only seems to be giving fairly gentle pushes to his 'gyroscopes' and there's still a fair amount of oscillation due to precession. I'm not sure how much this would help to stabilize a baloon capsule. It might just replace some 'slower' movements with higher frequency oscillations or even partiall replace them. The cure might just be worse than the disease, but that's just a top of the head thought.

In most gyroscopic stabilization systems I'm aware of, a stable inertial gyroscope platform with the gyros isolated from the forces on the vehicle by gimbals is used to produce pointing error signals which is then used to produce correcting forces via the vehicle's means e.g. rudders elevators, ailerons, wheels, reaction control jets, etc. Kind of a combination of an inertial guidance system and cruise control/auto-pilot.

So it seems to me, and I might be completely wrong here, that something like this might be made to work for a balloon providing we had some way to generate correction forces. It might be tough to model this since the capsule itself is in part the weight at the end of a pendulum suspended from the balloon, and the force vectors along the tether would seem to be hard to analyse.

And even if this were feasible it would also cut into the budgets for weight, power, and co$t.

Again just my thoughts, it still might warrant some thought.