The difference with Geany is that it uses the GTK+ Scintilla backend even on Windows, rather than the "native" Win32 Scintilla backend like Notepad++ does, so I don't think it would be possible to use DirectWrite.
Without testing, I'd wager the difference between Linux and Windows is that on Linux you're using a GTK+3 build whereas the official Windows installer uses GTK+2. If you wanted to test that theory you could try building on Linux and passing `--disable-gtk3` when running the `configure` script to force a GTK+2 build.