[irl_zebra]

Around 25 seconds into the video you can see how thick the cable is. I would guess probably an inch thick. With regular wire rope, the breaking strength of that diameter would be in the neighborhood of 80,000lbs[1] with the safe load strength closer to 16,000lbs. I'm guessing with regular maintenance and checking, it would be exceedingly rare to have a mechanical failure.

Additionally, the occupant is harnessed into the chair, bolted into what is essentially a spherical roll cage. Even with failure, I'm guessing there would be a crash but no serious injuries.

[1] - http://www.engineeringtoolbox.com/wire-rope-strength-d_1518....

[TrevorJ]

It's more about how the cable is managed in terms of slack, keeping the cage from flipping over, etc. I agree with you, the cable itself is an unlikely point of failure.