Ok, quick summary.
You launch a receiver application. Think of it as a web page, which links in our receiver SDK which will allow you to send pause/play/seek commands to your video. Ultimately, this can almost be as simple as:
// Initialization from our samples, redirecting all commands to mediaElement which I can't remember off the top of my head right now (sorry)
That is the thing you need to host somewhere and give us the URL in the "receiver URL" field. Of course, this is strict basics, you can do a lot more stuff in your receiver.
After that, in the sdk commands, you can call an Intent.Play on media router, or call our load message in the CastSession (there are two ways to talk to Chromecast. Pure media router, which is fine for super basic media, and Cast).
The URL of the media you pass to load can be anywhere, including video from your local storage, or, as we see here, from a web server running on your phone. At that point, you can seek, pause, volume if you have the UI elements to control them.