Generally speaking, no, you only have to follow the laws of the county where you are resident. I don't know why Project Gutenberg is taking any notice of the court case at all, although it probably should warn its contributors not to work on projects that aren't yet public domain in their own countries, to avoid any risk of legal action.

In this case the legal situation seems clear. The case is about several books written by Heinrich Mann, Thomas Mann and Alfred Döblin, who died less than 70 years ago, and all their works are still in copyright in Germany. However, copyright law in the US is more complex, and their works published before 1923 are public domain there.

Project Gutenberg has every right to publish these works from a web server located in the United States. If Germany doesn't like it, it can order that Gutenberg's website be blocked, like is already done with sites like The Pirate Bay in many countries, and with many other sites in restrictive countries like China.