Embedding video hero loop with a link

My WP theme doesn't have an option for embed codes for a hero video (silent loop), but instead has a place for me to paste a video URL (not code). This works with YouTube (link to the public video), but I can't get it to work with either Vimeo or Wistia. Am I missing something? Is there a special URL I'm supposed to use for them or is it the same as the public-facing url?

Many thanks for any ideas.