Each country has their own laws, and decides what type of investments can be offered to their citizens. I'm just not sure what you need this information for, and how it will help you?
US doesn't "have" any stocks listed on their exchanges, but exchanges simply list stocks of any companies that want to be listed, and that meet their and US regulatory (SEC) requirements. So companies that want to be listed on US exchanges will simply do all the work required to be listed.
And Chinese and other foreign companies want to be listed on US exchanges because this is the purpose of issuing a stock - to be listed on popular exchanges and have best access to investors. US stock market is the largest, most liquid, well regulated, and provides great or expanded/additional access to investors.