Is there a way to use GrabzIt in a ASP.NET Windows Application rather than a Web Application?

Yes you can use the SaveTo method in the ASP.NET library. To do this simply do something like:

string filepath = 'images/result.jpg';
GrabzItClient grabzIt = new GrabzItClient("Sign in to view your Application Key", "Sign in to view your Application Secret");
grabzIt.URLToImage('http://www.spacex.com');
grabzIt.SaveTo(filepath);