IANAL, but perhaps. The following paragraph actually states, that if all your content is password protected and you only give this password to personal acquaintances, then you clearly don't need an impressum. ( Along with two other examples, which also not very helpfill.)
The problem with this law is, that is says something about a page with some baby pictures ( so that grandma can see her grandchildren), and something about media corporations. However it simply does not address the case of a private blog, were the audience is not personally related to the author, but the author does also not try to make money with it.