Chinese (people)?

"Chinese" (and other adjectival forms ending in -ese: Vietnamese, Nepalese, Balinese, Japanese, Burmese, etc.) would seem to be the exception to the rule in that they can be used with or without the definite article.

Why? Well, I'd never thought about it before, but I suppose it has to do with two things:

a) The words can't be made plural (no such thing as "Chineses"); whereas when we say "Brazilians" or "Germans" we've magically transformed the adjective into a noun simply by adding an 's.' For this reason your example

I find it strange that for other nationalities the word 'people' is generally left out. Example: Americans like to drink tea.

is muddled. Of course we can't say "Americans people," because "Americans" is already a noun. We could, however, at least in theory, say "American people"...but we don't because we have the handy, unambiguous 's' form already.

b) Where one can't make a noun describing a nationality by adding an 's' to the adjective (e.g. "French" doesn't become "Frenches"; "Danish" doesn't become "Danishes"...unless you're talking about a pastry) English has developed irregular forms to describe those nationalities: Frenchmen, Danes, Spaniards, Finns, etc. English used to have such a form for the Chinese, "Chinaman," but somewhere along the line it was decided that the term is offensive.

An afterthought: In the classroom, I'd strongly encourage students to use the second form ("The Chinese like to drink tea") as both stylistically superior to the other two variants, and as a great deal more common.

And, since you asked for a 'rule,' I'd formulate it thus: "If an adjective describing a nationality ends in a 'z' or 's' sound (Chinese, Vietnamese, Swiss) it can't be made into a noun by pluralization, but can be treated as a noun either with or without the definite article. Alternatively, one can keep it an adjective and add the word 'people' to achieve the same meaning."

There is nothing useful to add to what zashibis said, but I'll add this useless bit: At times in the past, "the Chinese" was misinterpreted by some English speakers as a plural in -s of a singular Chinee, as in Bret Harte's poem "The Heathen chinee".

(The wax under Ah Sin's nails would have been used for marking particular cards,)

If saying "people" in this context you need to define the statement more for the sake of accuracy and clarity rather then for correct grammatical use.

I can't make the point using your example as it is too general but this works
"The Chinese people of Han ethnicity make up the largest ethnic group in the world"