Inadequate protection? They already have tested the HHQ-9 along with the 3D search radar aboard the Type 052C years ago. The HHQ-9 with a slant range of 200 km and a maximum service ceiling of 30 km (better than the European Aster) would be probably the most capable naval missile aside from the SM-3 and the S-300.
The FL-3000N is used to intercept missiles, and it has been installed on the Varyag. The HQ-9 intercepts aircraft. The author obviously didn't that into account.
Then again, for the final layer of defense, there's the 10 barreled Type 1030 CIWS that can fire over 10000 rounds per minute, much superior to the Phalanx and Goalkeeper CIWS weapons.
The BrahMos missile's speed does not increase its capability, and instead, makes it much easier to track and shoot down. The BrahMos will have a very high RCS (large size), very high IR signature (supersonic speeds and engine), lacks terrain hugging (which makes it even bigger on radar), and lacks the anti countermeasure maneuvers. Its only source of radar guidance also makes it prone to jamming. That's why the US and China use subsonic missiles that use pop up approach and various methods of guidance.
The BrahMos wouldn't make it within 200 km of the carrier before it is intercepted by the HQ-9.