Okay, I'm not going to have time to convert this to LabVIEW anything soon, so let me explain what needs to happen.
First, open up the file MainForm.cs in the example directory. You can just use Notepad, because VS.NET tends to hide auto-generated code - and that is just want you need to see here.
The way to understand this is to think of the .NET Container as the MainForm class. If you read the code, you see that the first thing done in the constructor is to call InitializeComponent. In there, the constructor for the GraphControl is called. As I said earlier, the .NET Container in LV does that for you, so you need to start on the next line.
Notice how many properties are being set? That is what you need to do also. I'm not sure whether all of them are critical for your application, but at least you can see everything that is being done in the example. Note that you only need to do the ones on the graph. At the end of InitializeComponent is a few properties for the MainForm itself. You can skip that.
Now InitializeComponent is done and we return to the MainForm constructor. Notice that it now makes calls - first to set the background property, then to load the libraries and then all the shape stuff. This looks like what you had in your VI, so my guess is that the properties in InitializeComponent are the key items missing (such as setting the size of the control, etc).
Give that a try and let me know how that goes.