China is not a socialist country, not anymore. It is merely another capitalist country under a merely symbolic red banner. The fact that affected children, their families actually, have to pay for their health care highlights how much burgueoise is modern P.R. China. Healthcare has always been public in any other socialist country, as well as in many capitalist ones, as it is a basic guarantee of citizen equality. But healthcare is not the only indicator: private business have become more and more powerful, unionization is restricted and state-controlled and there is an ongoing internal colonialism draining rural China.
In any case, they have a major problem: corruption. Ok, corruption can be found anywhere but when there is transparency and the media has enough freedom and diversity to expose it, it becomes quite limited. Additionally autocratic governments reduce the faith of the people in them, even in good times, and make cheating legitimate.
I have got now and then into some discussions on the different moral values of Chinese and Westerners, on how different can be the concepts of "guilt" and "shame" and so on. But I do not believe there are real moral differences or that these are important: there are cheaters and corrupt people everywhere, the real problem is that the public interest is against them and therefore they have much more problems if they can be exposed and if their political support can suffer from any corruption scandal like this one. That's why capitalist countries have tended (not always but often enough) to create republican regimes with guarantist schemes, such as human rights, independent judiciary, regular elections and things like that. These elements just add to public confidence and somehow guarantee that the worst abuses are less likely to happen. In fact I would dare to say that these have been central elements in the overall success of Capitalism worldwide, specially in its historical confrontation with the "Socialist camp" in the Cold War. The autocratic regimes of the USSR and the like could not prevent nor tackle corruption because there was no internal opposition, no semblance of free press and no independent judiciary. Eventually the corrupt and stagnated Soviet bloc had to collapse.
China has adressed in all this time only the issues of economical competitivity: it has become largely a capitalist country, able to challenge somewhat the hegemony of the USA that way. But it has failed to adress the other major issue, or at least it has not adressed it with enough determination. Without any control other than the also corrupt bureaucracy, in the long run corruption had to become a major problem and make the contradictions show up.
I guess that this outraging scandal may shatter somewhat the fundaments of the CCP regime. I don't know how far this patent crack will damage the system itself but it has definitively damaged public credibility a lot. If this doesn't make the system change quite drastically, there will be others, no doubt, and they will eventually cause the fall of the one-party system. Excuting a handful of corrupt officials, as has happened before, may sound like an exemplary measure but it will not correct corruption, specially if state censorship keeps being used to hide the problem. And this will be the case unless things change radically because if anyone has enough power to bury such a major public health scandal, that person will be almost unavoidably bribed and put at the service of the corrupt interests.
Personally I think that it is unavoidable that, as China becomes more and more burgueoise, it will find itself in the need to organize a burgueoise political system. Moreso if it has great power ambitions.
I don't dare to forecast timelines but change seems unavoidable one way or another.