Now I have de-installed Net Desktop runtime 6.0.6.
Than installed .NET Desktop Runtime 6.0.3, (exactly the version ArcGis Pro claims to be necessary)
Than rebooted the complete computer.
Result: ArcGIS Pro refuses to work,: .NET Desktop Runtime 6.0.3(!) is missing ...
Than installed latest version .NET Desktop Runtime 6.0.8 on top of 6.0.3.
-> ArcGIS Pro is running
ESRI owes me the equivalent of 3 hours of work due to misleading chatter in the tone of command ("... you MUST install...").