There are definitions for this title, which covers "executive branch" and "dependent child" among other terms, but not "news and communications media". When the law was passed, there were no web pages, so the matter is not addressed in the law, nor can we narrowly discern an original intent. The Ethics Office currently simply recites this restriction without any interpretation.
On May 15, 2000, CJ Rehnquist gave a speech which touched on this question (federal judges filing financial reports). There was an incident where some organization planned to disseminate financial information about all federal judges on a website. He reports (reflecting the conclusions of the Judicial Conference of the United States) that despite the well-meaninged desire of the Financial Disclosure Committee to withhold this information, the decision was not supported by the statutory language. As for defining news media, he opines:
Congress specifically provided in the Ethics in Government Act an
exemption from the prohibition on use of the reports for commercial
purposes to "news and communications media for dissemination to the
general public." That is to say that the news media can use the
reports for "commercial purposes" to disseminate the reports to the
public. And there are no exceptions to this for the Internet.
So in the view of some justices (ones whose opinion is not to be taken lightly), being an internet news medium does not render you not a news medium.