"like" is just a marketing label for the button/link. The actual function of it is to increase the visibility of the story. A lot of people have figured this out and use the facility for what it does rather than how it is labeled. I see this on FB a lot, too.
They like the post alerting people to this fact. The like it to share it with more people, making them aware. They aren't liking that China is doing this.
Liking that something is posted is not the same as liking the news.
You need to also assume that filtering the web increases 'social stability'. For many young people in China the amount of government interference with the web is literally their number one complaint.
By young think 15 not 25. The problem is not so much they are going to create a revolution today, rather the government is poisoning the well by eroding peoples trust.
That's what all the dictators say. "We need to maintain stability, so keep doing what we tell you. Don't you dare even question us - for the sake of our society, of course."
Actually, its the other way around. Don't even dare to mention stability or you get lynched in the West.
Ask people in Rhuanda/Burundi what happened when their dictator president got shot down. Or in Somalia. Or how the real situation in Iraq or Afghanistan is. Sometimes stability actually is paramount. It's even empirically measurable and relates to average household income. But I don't want to bore you with science on the topic. There are many books and papers on the topic. And its not just theory, I am living in developing and "unfree" countries for many years to see the practical part as well.
Stuff's not just "black and white" -- there is a lot more to it.
A few good reads on the topic are F. Fukuyama "Trust: Social Virtues and the Creation of Prosperity" and P. Collier "The bottom Billion" and "Wars, Guns and Votes: Democracy in Dangerous Places".