I looked at the site, but I have no idea what it is or what it costs. Total marketing failure.
https://store.google.com/us/product/chromecast_google_tv_com...
That page is a bit better at explaining things.
The lack of that feature is my biggest gripe with the current dongle. The Cast protocol is a pain in the butt in terms of apps that support it.
I don't know about this device, but what you are describing is the antitheses of how chomecast is intended to work (or at least it was, from the beginning of chromecast to the last time I checked).
The idea is that you never stream anything from your phone, but rather your phone is a remote control and service authentication device for the chromecast.