First, this functionality is limited to the Polaris Office app (iOSAndroid). The third party productivity suite prides itself for working best with all sorts of Office documents. So to use this functionality you’ll need to import your documents to Polaris. You can do it using the Open inmenu in iOS 8, the share sheet in Android, or just import documents to your account via the web.
Also, because Polaris is so focused on “the cloud“, you’ll need to sign up for an account. Annoying, yes, but at least you won’t lose your documents once that’s done.
Start the app and make sure Chromecast is enabled, running, and connected to the Wi-Fi network.  You’ll now see the ever familiarCast button in the top-right corner. Tap it and select your Chromecast.

Now, browse the files stored in the app and tap the one you want to stream. The app will ask if you really want to stream it to Chromecast; authenticate to continue.
Now, your Chromecast will show a loading screen (for a bit too long if I’m being honest), and your document will appear on the TV.

Take a look at the device in your hand. You’ll see a D pad and other navigation buttons on the top half and a touchpad on the bottom. You can swipe the touchpad to scroll and zoom in on Word documents.