The problem is the version of Windows 10 that the “MonoGame Windows 10 UAP” template targets. When MonoGame 3.4 was released, Windows 10 was still in a pre-release state (Beta? RC? RTM? Don’t remember). The templates that were bundled with MG 3.4 target that pre-release version of Windows 10. The current Windows 10 SDK does not target the pre-release version that the template specifies, and so it wants you to install the version of the SDK that DOES target the pre-release.
Therefore, the solution is to manually edit the csproj that was created from the template. Or, make a blank app and add the MonoGame references.