I fail to see how this affects IANA or root DNS servers in any way (not to mention that IANA can be replaced by a non-US entity if it really comes down to that).
As for those companies, they'll work the same way as before outside the US internet. Regrettably, because the world would be a better place without them.
This was a direct response to the commennt "I don't think there's any reason for us non-US-Americans to care at all about the US internet."
This change doesn't directly affect IANA, etc, but it will likely have knock-on effects which hurt everyone.
"IANA can be replaced by a non-US entity" - This would, IMO, signal the end of the internet. "Look up www.google.com" "which one?"
Changes made to the "US Internet" are going to absolutely affect the wider world right now.