As I understand the background, the US wanted to make it easier to collect judgments when a party did not have assets in the country where the money was owed. At this point, no one was thinking about the Internet, and the treaty was probably not of interest to very many people. Beginning in 1995, the use of the Internet and Internet commerce began to expand dramatically, and some persons began to see that the treaty would have significant consequences for ecommerce. Lots of what is done on the Internet crosses borders. The main purpose of the treaty is to provide for recognition of foreign judgments.
Different combinations are possible.
You could be sued in China, but your rights might be based upon a US law, or the other way around. You could also be sued in the UK under UK laws, and if you lost the case, the judgment would be recognized in the country where you live. The treaty is designed to address nearly all private commercial litigation, so its scope is very broad. Individuals, organizations or firms can now be sued in foreign jurisdictions, but since it is very difficult to collect foreign judgments, people don't have to worry much, unless they have assets in that country. And, before the Internet became important, there were also fewer cases where what people did was considered of legal consequence in a foreign country.