That's pretty much the entire point of what people are calling hypersonic missiles. All ballistic missiles fly at hypersonic speeds. The advance is being able to do so at low altitude with maneuverability.

You are correct, but I should point out that Russia has described its Kinzhal missiles as hypersonic, when they are really more of a traditional ballistic missile fired horizontally. So very fast (Mach 10), but not as maneuverable as what the U.S. has been calling hypersonic.

Since the original story here does not provide many details, we can't know which side of that fence this falls on (assuming it is real).

Kinzhals being intercepted all the time could also be propaganda or missile defense having progressed more than publicly known.

It's not a great idea in war to assume your enemy is incompetent (even when they are).