The description of "non-tourist" Chinese is intended to describe persons that are of Chinese ancestry, and in these contexts, more likely than not, immigrants from China now living-in, and/or working-in a different nation, for example, France, Italy, or the United States; their (primary) purpose for physically being there is not tourism/leisure/recreation.

No, a person living in America who was born in China, or whose parents were born in China, could self-identify or be identified as Chinese, American, both (e.g. "Chinese-American"), neither, or something else entirely.

I think the implication is that these are people who trained in their home countries and were brought to Italy so the luxury brands could continue claiming a "rich history of Italian craftsmanship." In a way it's true but it's also lying by omission.

Yes. There's also an interesting tangential topic of so-called "counterfeit" or "replica" luxury goods where they can sometimes be unofficial items produced from the exact same factory, in-country, or abroad as "extra-runs", as well as items produced by those "skilled artisans" that previously worked at the official factories recreating the same items, using the same methods and materials, unofficially elsewhere.