Did you read the link?
"Although they will be closing new registrations for 3rd-level .name domains, all existing domains (including this website) and email redirects will remain indefinitely."
They were apparently planning on shutting down the whole TLD. They will be leaving it up for existing registrants, but not allowing new registrations.
No, they were not planning that. This is only about 3rd level domain as the paragraph you quoted says. Every other TLD don't sell those (afaik). Normally "someone.name" would be a domain, and they would own all the subdomains. .name allowed you to register "one.someone.name" and "two.someone.name" as completely separated domains with completely separated owners. I understand why they should grandfather in existing domains but this was just madness.