The crux of the argument seems to be whether German copyright applies to US websites served to German users; Project Gutenberg's view and the Court's view are below.

Project Gutenberg:

Q: So the court thinks that the presence of content in German means that courts in Germany have jurisdiction, regardless of the fact that PGLAF is entirely in the US?
A: Yes, that was the original basis of the claim for jurisdiction, which the Court accepted in their judgement. Since then, there some more recent decisions in the European Court of Justice, and other German courts, that support this theory based on a Web site being accessible from a country. Those other cases involve companies that actually operate (for-profit) in Europe, and cases between two European countries (i.e. part of the EU). They are not consistent with prior laws and cases, even in Europe, and also not consistent with provisions of the Berne Convention and other international law.
In addition, PGLAF has pointed out that Germany is widely spoken in the US (the third-most common second language), and also is widely taught in schools and colleges. PGLAF has no actual presence or activity in Germany.

Court Decision:

Reasons for the decision
The action is admissible and well founded.
1. The action is admissible. In particular, the District Court of Frankfurt am Main has international and local jurisdiction pursuant to § 32 ZPO (German Rules of Civil Procedure). According to § 32 ZPO, the court of the district where an unlawful act was committed has jurisdiction for suits brought against such acts. Unlawful acts within the meaning of § 32 ZPO also include copyright infringements. Along with local jurisdiction, this provision also governs the international jurisdiction of German courts. An unlawful act within the meaning of § 32 ZPO is deemed to have been committed both at the place where the offense was committed and at the place where the offense had its effect, so jurisdiction optionally applies to the place where the infringement was committed or where the legally protected interest was affected. A conclusive claim of facts substantiating an unlawful act committed within the judicial district is enough to establish jurisdiction. § 32 ZPO also covers claims for injunctive relief. Accordingto§32ZPO,ifacopyrightorrelatedpropertyrightisallegedlyinfringedby making the protected property publicly accessible via a website, the place where the unlawful act was committed isGermanyiftheassertedrightsareprotectedinGermanyand if the website is (also) publicly accessible in Germany. However, intended availability of the web presence in Germany (among other countries) is not a requirement (Federal Court of Justice, GRUR 2016, 1048, marginal number 18 - An Evening with Marlene Dietrich; cf. Regional Court of Hamburg, Judgment dated 06/19/2015 - 308 0 161/13, BeckRS 2015, 18942; Regional Court of Hamburg, Judgment dated 06/17/2016 - 308 0 161/13, BeckRS 2016, 12262).
These requirements are met in this case, as the works in dispute which are protected in Germany are indisputably also available in Germany. Also, the plaintiff has convincingly argued that the availability has led to downloads in Germany.
Apart from that, the first defendant’s website is also intended to target German users. This is supported by the fact that the website is partially in German, that the site offers German- language works, and that the first defendant explicitly strives to make the works available globally (“anyone anywhere”). This is not contradicted by the disclaimer in the first defendant’s website stating that users must verify if they are entitled to download the works in their respective countries. Rather, this disclaimer indicates that the defendants are aware that their website is also visited by users from other countries than the United States.