It is definitely OK to mean the Chinese people as a whole (as a nation): "The Chinese people have once again taken their rightful place among the most advanced nations".
On the other hand, I have heard it a lot as a 1:1 translation for 中国人: "Chinese people like to come here a lot, there are many American people in his team, ...", so I understand why somebody told you that was Chinglish :-D. Often, a different construction like "A lot of Chinese (tourists, travelers) like to come here" would sound more natural to me when talking about individuals.
Then again, "what do British people eat?" - sounds perfectly fine. "Chinese people like to eat rice, American people like to eat pizza" - sounds like Chinese English to me :-D. Wow, this is more complicated than I thought! Maybe it is the stereotypical overuse of "country + people" that makes me think that way (sometimes also giving rise to incorrect formations like e.g. "Germany people" for "German people").
Sorry for the many updates to this answer - as I was thinking about it I realized that it is a bit tricky: even for individuals "Chinese / Spanish / etc. + people" can be OK, but if you do it in every sentence then it has a certain Chinese ring to it, at least to my ears ;-).
Thanks for your comments. I always keep in mind that I should not take so seriously about a certain expression in English. What I focus on is speaking naturally. For this topic, what I worry about is that my expression is not natural. I really recognize that some expressions are just fit for specific situation which is not just about language itself, but also is about the people, the regions. For example, some expressions are accepted in the south of China, however those are not accepted in the north of China.