I don't think that kind of thing would ever fly here even with the harness. Safety isn't exactly the Chinese government's number one concern.
These same kind of ropes courses exist and are being built all over the US, particularly in the east coast. I have done around 8 of them in my state alone and have seen many more. The 3 courses at SDL are far from the most difficult (not a bad thing, I'd expect that in this situation), but they're the coolest-looking I've ever seen.
As
@DisneyDrum pointed out, the person wears a harness with a rope attached. That rope connects into the "track" above and moves with them as they move along the course. These are actually very safe and efficient, because since you always attached to the "track" above, there is nearly no way you could possibly actually fall, and fewer safety people are needed as opposed to the older types of courses. Of course you may have a minor fall, but the rope catches you, and so you are usually able to climb back up onto the obstacle (and if you can't, a safety guide helps you). The most common ways you could really injure yourself are by pulling a muscle or banging into something.
All real concerns, but there are safety concerns with anything. A person could trip and fall getting out of a ride, or, well, fall into a gorilla cage. These ropes courses are probably safer than playgrounds. Sure, they're nerve wracking, especially if you're new to them. But safety-wise, I don't think there's much of an issue in the US, and the abundance of existing ropes courses proves that.
So it's certainly legal. I think there would be too many other problems for it to operate in a Disney park here simply because of demand that far outpaces capacity. Each person would also have to sign a waiver before they begin. It would likely be an upcharge thing, or at best, advanced reservation.
In China though, I think it'll be fine to operate, at least under their current laws. I love that Disney went for something unique and love that it's included in the price at SDL, and I hope that never changes.
I'm also fond of courses with a single direction that are themed (or go through a forest), as opposed to the square metal structures that seem more and more common nowadays.
TL;DR: It would fly here because it already does.