It uses small, dry plums called Zwetsche or Quetsche or sometimes called German Prunes. Juicy plums would flood the cake with juice.
A couple of examples of Zwetsche plums are Pozegaca and Gras Romanesc.
Pozegaca is notable for being the plum-of-choice for slivovitz plum brandy, being cold hardy to zone 4 and blooming late, thereby avoiding late spring frosts.
Gras Romanesc is notable for having a very high sugar content and is originally from Romania.
I am on the verge of ordering one of these two trees because the pictures of the plum cakes look so delicious.