I found a bit of a discrepancy. On the one hand, in the Longman dictionary, the word 'media' goes with 'the' in expressions like 'the news media', 'the mainstream media'. On the other hand, through Google search, I found out that expressions like 'Chinese state media' go with no article. Please explain.
Plural words, like "media", do not always require an article. It depends on whether or not you are referring to something specific.
- Horses eat grass. (Horses, in general, eat grass.)
- The horses eat grass. (These particular horses eat grass.)
If you say, "The Chinese state media" you are referring to the specific media operated by the Chinese state. However, you can say, "Chinese state media" to refer, generally, to media operated by the Chinese state.
You should also keep in mind that newspapers (if that's what you are reading) always try to conserve words where possible, so if a phrase doesn't really need an article (such as "Chinese state media") a newspaper writer will often leave it out.