Net neutrality in the USA affects everyone because it will shape the future of competition on the web in one of the largest and most important markets. Basically, entrenched giants will be much harder to disrupt across the globe, because of their huge incumbent advantage in the USA.
A startup trying to disrupt Google, Facebook, Netflix, etc. will have a much harder time succeeding if it doesn't have equal/fair access to the American market. Added to the fact that historically most web startups come from the USA, and you're talking about a potentially huge decrease in total innovation on the web.
The domain was originally administered by the United States Department of Defense, but is today operated by Verisign, and remains under ultimate jurisdiction of U.S. law.