I'm sure it's not misunderstanding. But the claim is from a later CCTV interview for the CJ-1000 crew, rather than directly from the parade. My bad. I've already reedited my last post.
You can watch the following CCTV interview video:
Also the CCTV transcript for it:
It indeed claims it can attack systems in the air precisely.
The narrator said "体系节点目标", meaning "System Node Targets". For aerial context, this can certainly refer to enemy airbases and facilities & infrastructure (e.g. radar sites, communication antennas, SAM sites) which support the operations of the enemy air forces, not necessarily (and definitely not, IMHO) enemy aerial assets.
And sorry - Why would you need multiple-100 kilograms of warhead powered by a massive hypersonic cruise missile just to shoot down an enemy AEW&C aircraft, all when one or two ULRAAMs with only double-digit kilograms of warhead each is/are already sufficient to do the job?
Can you explain the rationale, or did my high school physics failed me here?