If you want to use the current versions of the .NET wrappers for the VSTS REST APIs in a .NET Core application, you'll need to add the following to your *.csproj file to allow NuGet to fallback to using PCLs based on profiles:

<PropertyGroup>  
    <PackageTargetFallback>portable-net451+win8</PackageTargetFallback>
</PropertyGroup>