Google already has the capability to remove results, so they do not need to be "enabled" by EU law. I'm not really sure how you imagine this works, but the "right to be forgotten" refers to various legal frameworks in the EU for forcing companies to delete data that pertains to an individual.
It doesn't actually. There are no laws that create or define the right to be forgotten. It was a "right" created out of nothing by a new court interpretation of a very vaguely worded part of the ECHR. Before the court invented this right nobody was even talking about it.
I don't think they're happy about it. They've funded a lot of anti-DMCA stuff under "chilling effect" branding. The DMCA is a horrible law, so I don't think we should use it to justify similar takedown behavior under other laws.
