From Vimeo Support:

“Users might not be able to cast from the ASO site because Vimeo currently does not support casting Vimeo videos embedded or on vimeo.com, from the Chrome web browser to Chromecast. The only official method of casting Vimeo videos to Chromecast is with the Vimeo app for Android or iOS. Users might be able to do it with the direct link to the video on Vimeo instead of the embedded version on our site.

Some add-ons or extensions for the Chrome web browser (on both desktop and mobile devices) may enable this functionality, but these methods are not officially supported by Vimeo. That means the set up of some user’s browsers may allow it to function on site but it isn’t meant to so Vimeo is unable to make it also work from the ASO site’s embedded player.

Vimeo hopes to provide casting ability in the near future! Keep an eye on their blog for updates: https://vimeo.com/blog.”