Whatever the case it is better than a Zumwalt class destroyer and packs more anti-shipping firepower than the majority of Arleigh Burke's (Flight IIs) which never had dedicated anti-shipping missile launchers installed and use surface to air missiles as a poor quality substitute anti-shipping missile.
Luckily the Japanese install anti shipping firepower on their 40 odd destroyers.
I think one area where the Chinese currently hold an advantage with larger ships is that they can store anti-shipping missiles in VLS whereas your average American RGM-84 or Japanese Type 90 anti shipping missile is located in separate canisters that can't be easily reloaded.
Older US ships with box launchers had up to 24 anti shipping missiles (8 in Mk16 box launcher + 16 reloads), new ones have 8!
So you can load up a Chinese destroyer with far more anti shipping missiles than an American Ticoderonga or Arleigh Burke Flight I or Japanese destroyer (Kongo, Atago, Maya, Akizuki etc).
The other interesting thing with western ships is that despite the size of the ships growing from 5000 tons to 10000 tons+, there has been no increase in antishipping firepower.
Eg those latest Japanese 10,000+ ton Atago and Maya destroyers still only carry the same number of anti-shipping missiles as a 4000 ton Hatsuyuki (ie 8 missiles). Same applies to say English Type 45 Daring class destroyer or whatever.
The emphasis in the west over the last 30 years was air defence at the expense of anti shipping and anti submarine capabilities (strangely as "enemy" submarine capabilities grew over that time far more rapidly than aviation capabilities).