The Chinese weapon is ground launched, exactly as I stated. Sure you can boost such a weapon up above most of the atmosphere in order to get longer range, but the downside is that higher altitude flight paths make it easier to detect and counter.

AFAIK, there are no publicized counters to partially orbital hypersonic glide weapons in their glide phase due to their maneuverability and speed. Perhaps THAAD - but it may be difficult to ascertain the target when a weapon can glide halfway across the world

Well in theory the RIM-174 (SM-6) has some limited ability to intercept hypersonic glide weapons. Although obviously that's never been tested.

There are counters to hypersonic glide weapons beyond shooting them down. If you can detect it early enough then the target ship can change course and try to evade. The sensors on those missiles have very limited field of view so if it's not receiving a real time target track data link for course correction then it can be possibly be dodged (depending on how many are incoming, weather, and other factors). Even if the target can't evade, a bit of advance warning would at least allow for cueing EW countermeasures.