The reason to get the DNS provision into law is to shut
down websites operated from outside the United States
where the US does not have jurisdiction.
Could more accurately be stated as:
The reason to get the DNS provision into law is to keep
American's from accessing and funding websites operated
from outside the United States OR where the US does not
have jurisdiction (foreign TLDs).
The site can (and most likely will) remain up for the rest of the world. Just not those using US-based name servers and ISPs. (...IANAL)