What blows my mind is that you cannot connect to a Chromecast from the desktop client. Apparently there is no official desktop SDK for Google Cast (outside of Chrome). So perhaps that is what really blows my mind. Errhm.
You can actually get the desktop client connected to your Chromecast in a roundabout way. What I do is connect to my Chromecast from the Spotify app on my iPhone, and then the option will appear in the desktop client to connect. I have no idea why you have to channel through the phone first, but it works perfectly from desktop to Chromecast once it's connected.