I believe it's exactly that thinking that CSIS was trying to check when they chose to translate and publish this specific article. They are trying to get analysts and policy makers to think through, and make an active decision on if they believe that China will treat military/militarized mega constellations as destabilizing in a nuclear/strategic sense.
It's fair to decide that that is not major factor, but it should be an informed decision. It requires looking at the nuclear risk issues that the piece raises, and finding reasons to dismiss them.
Even the best space comms system does not make your ICBMs invisible to your adversary, and does not allow you to shoot down your adversary's return salvo of ICBMs. Hence the mutually assured destruction is not going away, and the side starting an all-out nuclear war still cannot win. I don't see how anything what's available now changes this; do you?
What might be destabilizing would be long-range hypersonic missiles that fly relatively low (30 km above the surface, not 1000 km), so they can't be easily detected until it's pretty late, and can arrive from multiple directions. This is exactly the kind of weapon that is China apparently developing, BTW.
The article argues that space and AI dominance meaningfully threatens China's second strike (mobile land based ICBMs) survivability, which would bias China to act more proactively (ie, more hair trigger) in escalation scenarios.
Chinese and Russian developments (HGVs, FOBs, the Russian "superweapons" like Poseidon) are all destabilizing to an extent. But as long as none them challenge/hold at risk the US second strike capability (a robust C2 network and the SSBN fleet), they won't be massively destabilizing.
For what it's worth, HGVs that could strike the US from China still need to be launched off what are effectively ICBM class rockets. The launch signatures would almost certainly be detected.
And finally, let's not even get started with what Golden Dome would do to strategic stability.
There's simply no need to go pointing fingers right now. The reality is that all sides are taking various self-interested actions that in the absence of communication or coordination will lead towards less stable environments. No side has the ability to compel the others to not take these actions, and so the best we can do is try to anticipate the new operating environments and be ready for them as best we can.