It could be a bug, or it could be something to look forward to announcing at E3. Who knows.
Found in both the Xbox (beta) and regular Xbox apps, when you view game information on titles you own within the app and while connected to your console, there's a mysterious "Play from console" option present with the streaming logo.
It doesn't actually work right now, and we've verified ourselves that this is the case. You'll see the streaming bar appear at the top of the screen, but nothing else happens. It'll error out with some kind of message that says you can't do this right now.
Streaming to Windows 10 Mobile should be made easier by the recent announcement from Build that phones will be able to use the Xbox One controller. It'd also be another killer feature to add to the mobile operating system, and one a number of folks are surely interested in.
Microsoft wouldn't be the first to accomplish this, of course, with Sony already allowing buyers of its Xperia phones and tablets to stream PS4 games to their mobile devices and play them with the DualShock 4 controller. As with Xbox to PC streaming there are a number of variables that affect the experience.
There's also no guarantee this isn't a bug. The Xbox app is universal to both PC and phone and so something could have gone awry somewhere. But with E3 right around the corner, add this to the list of things we hope that Phil Spencer is "pleased to announce."