In day-to-day usage, it doesn't, at all. Who owns a domain doesn't have anything to do with where the traffic flows.
If I owned buttplug.io (which I don't, unfortunately), and someone sent traffic to me (by visiting the website), DNS would look up and return the IP address of my server, and that's where the traffic would go.
In theory, since the owner of the TLD controls the root DNS servers, I guess they could hijack the DNS to send the traffic to their server instead. We would know if that happened though.