So, say I buy a domain from Register.com and then manually post it on my Facebook that I bought this, that isn't Register.com's fault right?

This seems pointless because you could still just encourage people to do it manually, in another part of the purchase flow, or maybe even a week or two after? It seems to me that the patent just blocks you from having an official Facebook share button or Tweet (or something like that) button on the checkout summary page.