Using SUA (an optional component) you can have a POSIX environment on Window, but IMHO, any first class application in Windows has to work as a "native" one, not pretending to be still in its *nix environment, and should not require any optional compatibility layer.
OK then, using this definition name a single native Windows application: I certainly can't. The lowest system call layer of Windows is not publicly documented - the lowest level access you can get is the interface exposed by NTDLL.DLL. Above that for what is usually regarded a "native" Windows application you have the Win32/Win64 API as implemented by WIN32.DLL. Most of the "native" facilities you are keen to emphasise are facilities in those compatibility layers that implement the public APIs rather than features of the underlying OS kernel itself.