Directive 95/46/EC (the Data Protection Directive) never specifically mentions "search engines", it talks about "controllers" of personal data. The ECJ ruled (Case C‑131/12) that search engines such as Google count as controllers of personal data, and thus are subject to the "right to be forgotten" under the Directive. But clearly the Directive is applicable to many other things than search engines, so the "right to be forgotten" cannot be restricted to search engines either. (Newspapers should be exempt because article 9 of the directive has an exemption for "the processing of personal data carried out solely for journalistic purposes or the purpose of artistic or literary expression", but search engines don't fall into that category, and other web sites may or may not either.)
The court judgement - http://curia.europa.eu/juris/document/document_print.jsf?doc... - paragraph 26 says "As regards in particular the internet, the Court has already had occasion to state that the operation of loading personal data on an internet page must be considered to be such ‘processing’ within the meaning of Article 2(b) of Directive 95/46" - so by the Court's reasoning the Directive potentially applies to any web page, not just search engines.