Regretfully, this is not a feature offered by the Content Area Modal. This requires the use of Vimeo's API. Integrating that would require custom development which is outside the scope of our support.
An alternative option would be to use our Lighbox shortcode. It has streaming video autoplay support so adding the autoplay parameter
autoplay=1 to a Youtube or Vimeo video URL will autoplay the video upon activating the lightbox. See https://youtu.be/a81SNAi_VIE
[image src="https://picsum.photos/200/300" link="true" href="//player.vimeo.com/video/84751465?autoplay=1" lightbox_video="true"]
I'm using an image in that example above but you can use a button also.