The holder of those domains has been known for a while to be Sirius (Martti Malmi)
This isn't so much about figuring out who Satoshi is as it is to showing he IS alive.
It is known that Sirius was given ownership of bitcoin.org but I did not see any mention of bitcoin.net and bitcoins.org. It is possible that when Satoshi handed over bitcoin.org to Sirius he also handed over bitcoin.net and bitcoins.org as well. However, bitcoin.org whois shows it moved Registrar and to a Finish ownership of some sort in 2011. Bitcoin.net and bitcoins.org did not follow the same path. They sat at Anonymousspeech until a couple months ago. This implies that if Satoshi passed ownership of those domains to Sirius along with bitcoin.org in 2011, Sirius continued to keep those domains at Anonymousspeech, paying the higher markup fee charged by that registrar, while moving bitcoin.org to his own registrar. Further, to do this Sirius would have needed to bother with setting up at Anonymousspeech OR satoshi would have given Sirius his own username and password to continue with the registration renewals at this registrar. The latter is *highly* unlikely as Satoshi used an email address provided by the same registrar for anonymous mail (vistomail.com is a webmail service of Anonymousspeech) that was likely tied to the same login.