To answer your question, out of the two it would be
'1. This week, however, the magazine did not have any Chinese news'
However it would be much better to say
This week, however, the magazine did not have any news regarding China
Or if there was a special section dedicated to news regarding China, or a feed from a Chinese news agency you could say
This week, however, the magazine did not have any news from China
My reasoning: There are Chinese communities outside of China. Also and especially in the UK, 'Chinese' is used to describe Chinese cuisine. And more loosely, 'Chinese' is used to describe the Mandarin and Cantonese languages combined.
Hope that helps.