There is no evidence to support or deny the notion of "hypersonic".
The author misquoted the CCTV announcer as saying"hypersonic". If you watch the CCTV video, the announcer only said "high speed", but did not say how high, it can be from Mach one (supersonic) to above mach 5 (hyper-sonic).
I don't know if there is a CCTV English version and if there is what was said there. But certainly the Chinese version did not use the word "hyper-sonic".
Given the existence of the supersonic YJ-12 and the sheer size of this thing, a Tsirkon counterpart isn't a bad guess. Would be cool to actually see the configuration (yes, I know about the seizure-inducing video with a blurry shot of it launching).
The nose cone if fully extended would close the nose inlet during take off. During flight, the nose cone would withdraw inwards, opening the inlet to allow the air in. That's how I suspect it might work.