> [The President] may declare a cybersecurity emergency and order the limitation or shutdown of Internet traffic to and from any compromised Federal Government or United States critical infrastructure information system or network […]
So we're talking about emergency airgapping federal/military networks, and whatever other domestic sections of the backbone are deemed “critical infrastructure.” It's quite an extreme measure, but there's no implication of claiming the power to turn off the lights for everyone around the world (or even in the US).