Could not include Esri.ArcGISRuntime, Version=100.4.0.0 directly into .Net Core 2.1 project. So went through standard .Net 2 class library, (i.e. made a class library to include the runtime, then referenced this standard library from the .net core web api project). Compiles, but when run gives:
BadImageFormatException: Could not load file or assembly 'Esri.ArcGISRuntime, Version=100.4.0.0, Culture=neutral, PublicKeyToken=8fc3cc631e44ad86'. Reference assemblies should not be loaded for execution. They can only be loaded in the Reflection-only loader context. (Exception from HRESULT: 0x80131058)