The question then is, how does this apply to search engines/indexers? I don't think it necessarily should, however since 'indexers' are not a recognized role in data processing laws, it takes some case law to figure these things out properly.
By the letter of the law, if something about me is indexed by google, they are processing my personal data and I have the right to ask them to stop doing that and delete it. Realistically though, this can lead to abuse by public people same as the DCMA does for companies.
So, still some work to be done. But I am glad that I have a legal way to force for instance a marketing deparment to stop harassing me with spam mail/calls. In practice, the threat of making a official request is often enough to motivate them ;)