Lets see...
1) (python.exe:1180): Gdk-CRITICAL **: gdk_device... : That is not an error. It's perfectly normal.
3) I don't have libgiognutls.dll or libgiolibproxy.dll anywhere in my system. It seems you are running a different version of PyGObject.
4) The paths have / and \ mixed together...
5) Did you run python from the Windows command prompt or from the WinPython Command Prompt?
6) To test if you have PyGObject installed correctly try running the following:
C:\WinPython-32\python-2.7.6>python
Python 2.7.6 (default, Nov 10 2013, 19:24:18) [MSC v.1500 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> from gi.repository import Gtk
>>> from gi.repository import Gdk
>>> from gi.repository import GdkPixbuf
>>> from gi.repository import GLib
>>> from gi.repository import GObject
>>>