Not really. While there are more cities in Germany with a system called U-Bahn only Berlin, Hamburg, Munich and Nuremberg have real U-Bahn-systems all the others technically are Stadtbahnen, Unterstraßenbahnen or simular.

But if course it’s up for discussion if the term metro should be translated in such a strict way, or whether it should be done more open to include other systems as well.

Edit: So at least if you follow the definition of the word Metro by the UITP the map is completely correct for Germany.