Ah, yes, guess you never wondered why all the dates on that website are over
a year old?

See http://wireshark.org/migration.html

Wireshark actually has really good capabilities for writing extensions, but
they aren't so much oriented toward embedding wireshark in another program.
You might have better luck writing an extension in wireshark which forwards
the data to your program for display.

If you must have wireshark embedded, I think you'll need to start by using
Gtk# for your GUI.  Then you would have to recompile wireshark as a DLL and
add an alternate entry point which creates the main window as a child of an
existing Gtk window which your .NET app creates.  Probably not too
difficult, but you won't have a clear upgrade path to incorporate future
wireshark features and bugfixes.