I am otherwise not an expert and am not invested in the idea of Fujian using either energy storage system but there's 2 data points:
1. The physics are there for heavy high RPM spinning objects. Steam turbines spin at typically ~2k RPM range, flywheels at up to 60k RPM. Even the US has recognized naval flywheels as an engineering challenge as late as 2022. The engineering and reliability challenges of the catapult on the Ford are well known.
The US EMLS' problem was never the root cause of its trouble, it is the AC archetect. Flywheel isn't the only thing in the system, American does not always make mistakes on everything.
The bottom line is that nothing be it capacitor or battery has the energy and power desity as flywheel to work for catapult. Capacitor has a the highest power density but lowest energy desity, battery goes to the other extreme, only flywheel stands on the right middle ground. It is not about who can do it, but limitation of today's technology.
2. In 2023, Ma Weiming specifically mentioned capacitors (电容器) applied to naval
EM launch technologies 15+ times but only mentioning a foreign (Japanese) flywheel (惯性储能) once as a comparison.
The above is a copy of his original article.
That paper 电磁发射技术的研究现状与挑战 talked about three types of EM 发射 tech. It is important to note and it is distinctively stated in the paper that 发射 includes three types of application, 弹射 (hundres meter range), 轨道炮 (railgun tens of meters) and 推射 (thousand meters, such as rocket acceleration), . All of the three are 发射 which can be translated into English as launch. But in Chinese only 弹射 is catapult launch for the CV. 发射 is used as a umbrella term to include any EM accelerating tech.
Ultimately in the paper (2016) by Ma Weiming, EM cat's key tech is Inertial energy storage, AKA 电机储能 (eletric motor storage), AKA flywheel. So regardless where people come from, Ma's EM cat uses flywheel as far as we are informed.