A nuclear warhead is a well known method of destroying an aircfaft carrier group. China just came late to the party and the journalists are all excited.
For example, this is an interesting video. BrahMos, in this video, is not supposed to carry a nuclear payload. The weight of the payload is specified as up to 300 kg. But if you look at Moskit which is officially nuclear-capable you read this:
320 kg (710 lb) explosive or 120 kt of TNT fission-fusion thermonuclear
Now, how hard would it be to mount a 300 kg warhead onto a 300 kg capable missile? Is it even conceivable that nobody in the long chain of generals, Russian and Indian, ever asked that question? IMO, BrahMos is advertised as a conventional weapon only because it's an international project. Everyone understands that you don't use these missiles against fishing boats. (But you can; look at the accuracy in the video.)
The new thing that China did here is simple. They used a ballistic missile, and as I understand it is minimally controlled in the descent phase. Its defense is only in speed, and in hope that it is correctly aimed and the target does not move appreciably fast and that the target does not shoot at the incoming missile with everything it got. This may be a valid approach, or it may be a flawed one. Without a test in battle conditions it's hard to say; after the test the survivors wouldn't be very interested in such trivia.
The implication in the original article was that the missile contained a non-nuclear warhead. So you really haven’t added anything new here. The quoted sentence admits that a nuclear warhead could do this. The purpose of my post was that a non-nuclear warhead couldn’t have that yield.
You also state the obvious, i.e. that a nuclear device COULD take out an aircraft carrier. Oddly - the BEST way for such a delivery is for the nuke to go off UNDER the carrier, not above it or near it. The damage to surface vessels even a small distance away from a nuclear detonation can survive at some level. You either have to deliver it right on top or right underneath (which is what nuclear tipped torps do). The nuclear tipped torp will break the keel of any major surface combatant and send it to the bottom instantly.