Google cast on Ubuntu 16.04

Yes, but the UI is not particularly obvious. Click the down arrow to the right of "Cast to" and click "Cast desktop". Later when you start the cast you get a choice of any application window or entire desktop.

From the Google Cast web store description (emphasis added):

The Google Cast extension enables you to find and play content on your Chromecast device from your Chrome browser.

[…] using your computer as a remote to browse for videos and to control playback.

You can also cast any of your tabs in Chrome to your TV, letting you enjoy sites, photos, or even video from the best screen in your home. […]

Since there's no mention of the computer desktop or other applications I'd say that Google Cast cannot be used as a general remote desktop interface.

There are however other applications for such a purpose, most notably

• VNC if you want to display or remote-control arbitrary desktop applications (though it wouldn't work well for video and audio content), and
• XMBC if you want to play back media from your Ubuntu machine on an Android device.

Both need a server software on the Ubuntu “host” system and a suitable client on the Android “client” (of which there are many).