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 it wasn’t working by the time reviewers got their hands on it.

The website wasn’t working for me earlier, but the wayback machine does have an archive of 6,640 users out of the 8,178 that seem to be on the website. Note that the wayback machine archive includes emails, while the current published version does not seem to.

https://web.archive.org/web/20251008141446if_/https://okstupid.lol/merged_details.json