Google supports and recommends using the schema.org on-page markup for videos. However it is not clear if this should also be done when embeddeding a YouTube video. Or really even a Vimeo video. Or is the schema.org only necessary when hosting the videos yourself?
schema.org is never necessary and you are free to markup (or not) whatever you wish, including third-party content. It's up to you if you wish to add markup or not — there's nothing saying you shouldn't. Feel free to use
sameAs to refer back to the original youtube.com/etc page.