I think it's basically because Unity doesn't define the compilation symbols you are using for multi-platform development:
Assets\Spine\spine-csharp\Atlas.cs(74,42): error CS1502: The best overloaded method match for 'System.IO.StreamReader.StreamReader(System.IO.Stream)' has some invalid arguments
This line shouldn't be even compiled for Windows Store apps, because of which you already wrapped it with an "#if WINDOWS_STOREAPP".
I chose the above approach with building the whole project into .dlls because I didn't want to figure out all affected parts of the code, but instead rely on your work and use your compilation symbols 😉