Trump ran under the principle that he stood for free markets and business. As soon as he got into office, though, he made it clear that he would use his powers to intimidate businesses as a way to control them. He publishes tweets about businesses when they do things he doesn't like.
After China forced Apple to remove New York Times app due to unflattering coverage, Trump is also likely to make decision that are unfavorable to the Chinese. He might just prove to his critics that his harsh words on China during his campaign were not mere rhetoric but he is in deed going to walk his talk.
No, I don't think that Trump is going to censor the media. I think one of the reason why people like him so much is that he just doesn't really have much use for the media at all. In the day's leading up to the inauguration, he is speaking to the American people directly through social media instead of using traditional media platforms.
The Chinese government does not grant freedom of speech nor the freedom of the press to its citizens. However, both of these rights are protected in the United States by our constitution. Therefore, even if a President Trump wanted to, he would be unable to force a news organization to remove content like China does.