I do not believe that you can. While semantically it looks like the div is loaded inside your page the styling and everything is controlled through vimeo. So the only way you would be able to style it would be if you had access to vimeo's css. There may be options though that allow you to change the theme of the embed or hide certain things.
https://vimeo.zendesk.com/hc/en-us/articles/224972808-Customize-the-video-player
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