Otherwise, it is limited to internet traffic from people within the European Union.
This rule was unclear in the beginning of the law implement, but there have been high court rulings clearing up the confusion.
See this, for example “Google wins landmark right to be forgotten case”: https://www.bbc.com/news/technology-49808208
There are limits to that due to contract law, but there are also limits how many rights one can sign away, especially when dealing with predatory corporations.
To give a less digital analogue: if you are robbed, your local police is the authority you talk to. They are not going to tell you that you need to find out who robbed you and talk to the police in their home town.
I am a dual US|EU citizen, but I am culturally American. I was trying to explain it from the perspective of Americans.
Thank you again for the clarification.