You can't use NetworkInformation's ping with TNet because when you ping a remote computer you don't go through TNet, and in most cases remote computers are not ping-able.
The code I posted lets you ping TNet's game servers, assuming they are listening to UDP traffic. To request a ping, use
TNManager.BeginPacket(Packet.RequestPing);
TNManager.EndPacket(remoteEndPoint);
...where "remoteEndPoint" is the end point of your server that you should already know.
Edit: Looking at the code though... there are further changes necessary in order for this to work as the "Ping" packet is handled internally inside GameClient.ProcessPacket, and there is no event callback for it which you'd want. I'll just add it to the next update.