Twitter offers a rich media experience for certain URLs that they call Twitter Cards. This displays images and video directly inline with a tweet, creating a lower barrier for enjoying the media that was attached to the post.
Vimeo OTT theme sites automatically add the code needed for these to appear. All you need to do is supply a Package with a cover image and a trailer. After that, you're ready to start sharing your Vimeo OTT site link on Twitter for the embed player to appear!