WIth Vimeo Plus account, how to hide/remove the “play” button in the middle of an embedded video?

You can now remove all controls

just wanted to update anyone new looking at this.
It now appears to be possible to have an embeded video without any of the controls, by using an experimental feature: background=1

Things to note

1. All player toggles and elements will be turned off (including the play/pause button!)
2. The video will automatically loop.
3. The video will be set to autoplay.
4. The video will be muted.

you can then use the js-api to control the video (pause, play, etc).

Example Embed Code

<iframe src="https://player.vimeo.com/video/76979871?background=1" 
   width="500" height="281" frameborder="0" webkitallowfullscreen 
   mozallowfullscreen allowfullscreen>
</iframe>

See the forum post here: https://vimeo.com/forums/help/topic:278001