The two phrases mean different things which are probably better illustrated using words referring to groups other than the Chinese. "The X people" refers to the citizens of a country while "X people" refers to an ethnic group or people from a geographical region.
Often these are basically the same group, think of "The French people" and "French people". However "The American people" refers to the citizens of the USA while "American people" could include anyone from Canadians to Chileans and Argentinians and all nationalities in between (but can also refer specifically to people from the USA).
It is possible to belong to more than one group. For instance someone could be ethnically Chinese and be a "Chinese person", be a citizen of the USA and so be one of "The American people" and by virtue of that be an "American person".
There are also cases where only one phrase can be used. "European people" and "South Asian people" both make sense, but "The European people" and "The South Asian people" are not really meaningful since both areas consist of independent sovreign states and there is no unifying federal state called South Asia or Europe. (There is the European Union but that is not a nation state).
It is always possible to say "X people" because a nation state is a region but it is not always appropriate to say "The X people" since not all regions are nation states.
The complication with "The Chinese people" is that there are two meanings: the people of the People's Republic of China (PRC) and the people of the Republic of China (RoC). Perhaps this might not be an issue inside the two states but it certainly applies outside. "Chinese people", however, applies to all Han and Chinese minority people wherever they live.
In additon to the above it should be noted that "X people" does not have to refer to all the inhabitants of a region or people from that region. In some contexts it can apply to a subset, even quite a small one. For example in a discussion of ethnic minority communities in London someone might say "Chinese people have strong communal ties".