Indeed, the Data protection directive is not about search engines: it is about privacy online in general and any web page published or plausibly controlled from within the European union is subject to it (and of course also to any IPFS page, although who controls it is harder to say). It has always applied to a lot more than search engines.
The "right to be forgotten" is a phrase used in the argument for de-listing, and later became the name for the ruling itself. This was however not a right that the court granted, but rather the court points out that the data protection directive stipulates that personal data shall be:
"""
(c) adequate, relevant and not excessive in relation to the purposes for which they are collected and/or further processed;
(d) accurate and, where necessary, kept up to date; every reasonable step must be taken to ensure that data which are inaccurate or incomplete, having regard to the purposes for which they were collected or for which they are further processed, are erased or rectified;
"""
and judges (in paragraph 93) that in particular, data that was once in compliance might not be at a later time.
It also states that the failure of the particular data in this case to be those things means the person described by them can invoke the right to object to the processing, in this case having personal data listed on a page as a response to a "search made on the basis of his name" (in paragraph 94).
It is not completely clear, but I think the query being judged upon includes only the name of the person, and adding a keyword relating to the particular year, or bankruptcy actions, would be enough to make the data "adequate, relevant and not excessive".