How can I replicate authentic German potato dumplings?
I am German, let me try to help, I've made many dumplings:

There are four types of potato dumplings. They are called Klöße in northern Germany and Knödel in the south, both words mean the same.

-Rohe Klöße (Raw Dumplings). These are made from raw grated potatoes. They are the most difficult to make. The surface is shiny and a bit slimy and you have pieces of potatoes sticking out, which gives them a rough surface texture, see image below. The inside is chewy and you can just barely feel the individual slices of potatoes.
They are soft, when you cut them they flatten and the surface is gluey and sticks to the knife.
The basic recipe is to grate raw potatoes (1 kg) into a bowl filled with water. Then pour the mixture through a cheesecloth and press the cheesecloth in your hands till the mixture is very dry. Let the drained off water stand for a few minutes, the starch will collect at the bottom. Mix starch and potato mixture. 

Boil some semolina (grieß), maybe 10% of the potato weight, in milk till it doesn't stick to the bottom of the pot. Mix semolina with potatoes and one egg and form dumplings.

Some people use sulfur to give the dumplings a whiter color
What’s the sulfur in dumplings for?

-Gekochte Knödel (Cooked Dumplings). These are made from boiled potatoes that are mashed while hot. Add about 10% starch and one egg yolk per 500g. These are simple to make.

-Halb und Halb, Thüringer Klöße (Half and Half). Mixture of grated and mashed potatoes.
Do as for the raw knödel with half of the potatoes. The rest is boiled and mashed while still hot, I have something that looks like a huge garlic press for this 

Mix the mashed potatoes and the dried grated potatoes and the starch. These dumplings don't use eggs or semolina, but you might want to add some extra starch if the dough is too sticky.

-Quark or Topfenknödel (Dumplings with fresh cheese (Quark)) 
Made from mashed potatoes with fresh white cheese. Tastes wonderful when filled with plums or apricots or with strawberry or rhubarb sauce.
Unfortunately Quark is extremely expensive in the U.S. 

The picture you showed looks like Rohe Knödel or Thüringers.

*Many people buy a mixture that comes in perforated bags that you throw into boiling water.

 These are ok, but the ones you make yourself are more fun.

*In Germany potatoes come in three color coded varieties, firm, mostly firm and starchy. For all kinds use mehligkochende Kartoffeln (starchy). These often have irregular shapes and break apart when you boil them. It won't work with firm potatoes.


*Often Knödel are filled with roasted pieces of bread.

*You always have to prepare a Probekloß (Test Dumpling) first to check the composition and maybe add some flour.

*In general the dough has to be sticky, use wet hands

*Some use egg yolks and some entire eggs.

*I am to lazy to get the starch out of the water, I use regular bought starch.

Make sure that you are using the right potatoes (starchy). To me it sounds you are using too much flour and the wrong potatoes. Better use starch instead of flour.