As patents are granted by national or regional patent offices, the patents are therefore only useful for protecting an invention in the country in which that patent is granted. In other words, patent is territorial in nature it doesn't provide global rights.
What is the gripe that the current US administration has with the
Chinese patent system?
China has been continuously placed in priority watch list since 2006, the reason for that reflects in the special 301 report is that china need for fundamental structural changes to strengthen IP protection and enforcement, including as to trade secret theft, online piracy and counterfeiting, the high volume manufacture and export of counterfeit goods, and impediments to pharmaceutical innovation. The concern expressed by US administration is such counterfeit goods making its way into US through various online sites.
If an inventor files (and obtains) a patent from the USPTO, but never
applies for a patent in China, does a Chinese manufacturer (not) have
the right to clone the product in China?
The product is patented in US but there in no patent filed in China then, the chinese manufacturer can clone the product.But, he cannot to export the product to US as there is patent protection. He could sell such product in china or any other country where there is no patent protection for that product.
Is there is no reciprocity in this regards? Is a patent sought &
obtained in China (not) automatically protected in the US?