I have done a small example of a desktop application, starting the YouTube app on the Chromecast device and playing a video on your TV. Using some Indy components and a couple of the new REST components that came with XE6. Not bothering with the API's from Google.
This example does not really have any real life usage - since installing Google cast in your Chrome browser or using the YouTube app on your phone would make more sense. So unless you for some reason don't use Chrome as a browser or do not have an iOS or Android phone, this example is not that useful - but it shows the concept.
And I think that the Chromecast is a nice $30 device, that like "almost" anything else can be accessed from Delphi :-D (Update: I might end up using Mozilla's cast device, if the rumors are true - see update at the end of post).