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?"
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.