Hi @fechaugger,
Well, it's not like there's actually a user-manual to how China's “Great Firewall” works
What I seem to have gathered is that through the state-owned ISPs, they can either block pages they don't like (DNS cannot be reached, 404 Page not Found), that kind of stuff...
Or, if it's a company that operates within the regulatory measures of the government's control over information, then from I've gathered from a CFR article about it, supposedly there is something called the Public Pledge on Self-Regulation and Professional Ethics for China Internet Industry
The government issued in May 2010 its first white paper on the internet that focused on the concept of “internet sovereignty,” requiring all internet users in China, including foreign organizations and individuals, to abide by Chinese laws and regulations. Chinese internet companies are now required to sign the “Public Pledge on Self-Regulation and Professional Ethics for China Internet Industry,” which entails even stricter rules than those in the white paper, according to Jason Q. Ng, a specialist on Chinese media censorship and author of Blocked on Weibo. Since Chinese President Xi Jinping came to power, censorship of all forms of media has tightened. In February 2016, Xi announced new media policy for party and state news outlines: “All the work by the party’s media must reflect the party’s will, safeguard the party’s authority, and safeguard the party’s unity,” emphasizing that state media must align themselves with the “thought, politics, and actions” of the party leadership. A China Daily essay emphasized Xi’s policy, noting that “the nation’s media outlets are essential to political stability.”
In my opinion, though this would probably require more research to make any formal proclamation, the big messaging platforms have a built-in backdoor in their software that allows the state censor's to monitor, track, edit and delete content as they see fit...
I also believe just like the NSA has these tools with Facebook and Google+, the Chinese have it with WeChat, Weibo, QQ, etc...
It's just part of the way the Hypertext Transfer Protocol (HTTP) is regulated by the various governments of the world to keep tabs on what goes on on the internet...
Every major country has some form of data-management agency... Though it would seem in China, they are really not that specific about who does what and how all of this gets decided...
That's why I proposed to find a Chinese company that already has experience with dealing with these regulations to craft the app... It would be far too complicated for a group of coders from America to make this app and unroll it in China themselves...
TLDR:
The less long-winded answer is yes, they have direct supervision over these media companies; the same way the US government has direct supervision over its own social media platforms through the NSA.