Their quick start guide confirms that it does stream from the Steam Machine.

Steam Frame includes a wireless adapater to provide the best quality streaming from your Steam Machine or VR-compatible PC.

Steam Frame: Official Overview and Quick Start Guide (@ 3:40)

Personally I am slightly concerned about their confidence in it’s performance with the Steam Machine if a reviewer somehow was told in some way that it wouldnt work, even though I’m assuming that was some sort of communication issue.