Furthermore, that would mean that this sentence literally states: a thousand-year period is one thousand years.

In English, we typically don't think about the morphemes that make up Greek/Latin-based words such as millennium (mīlle + annus). A millennium is a thousand years → a thousand years is a thousand years.

I wonder if this is the case in Vietnamese.

Thanks for this. Its interesting to see the hanzi/kanji for "thousand" and "year" in that word from which the Vietnamese derives, as well as the similarity of pronunciation with nián/nen and niên (meaning "year").

I think both are possible