Congratulations, you're using Internet Explorer. Google's Deskbar uses the WebBrowser control; Internet Explorer (IEXPLORE.EXE) is merely a frame window which hosts a WebBrowser. I've no doubt that the actual search HTTP access code uses the WinInet library.
Until Mozilla or Konqueror manage to become this embeddable, I don't think we'll see a Mac or Linux deskbar (not to mention that Linux has two major desktop environments, KDE and Gnome, which implement taskbar embedding in different ways).
I find it ironic, since El Reg is heavily in the ABM camp.