Vidyard allows you to push your videos to Facebook without ever having to download the files from Vidyard and then re-upload to your Facebook account.
This is different to sharing a player to Facebook. In this case, OpenGraph tags on the Vidyard player's sharing page will allow Facebook to render an inline player on the desktop version, but not on mobile.
By pushing your videos to Facebook, the videos are re-rendered using Facebook's encoder and displayed in the same way as any other video directly uploaded to Facebook.
The videos will, therefore, automatically play on all platforms assuming autoplay is the current method of how Facebook delivers video content.