If you don't have a personal library of movies and tv shows or home videos then Emby probably isn't for you. But neither is Plex (nothing against them) just being honest.
Emby supports a lot of functionality and while it could be made to work for your needs, really isn't the best choice for your needs. We would rather be honest with you and tell you that the functionality you want isn't are core expertise.
Emby (and Plex more sort of ) is geared to allowing your to create your own "netflix", "hulu" or "amazon video" type system if you have/own the video being broadcast.
If your intention is not to host your own videos or movies/TV shows on your ow server but only to "transfer" video from one device to another than you might just want to check out feature built into Google Chrome Browser.
With most OS and/or Crome browser you can send a video you have playing on a mobile or web browser to a dedicated device. In Google Chrome this is commonly called 'casting".
Emby can do this BUT if this is your prime directive in media than Emby probably isn't the best way to accomplish this.
So a direct question is. Do you want to stream your own media or is this not important and only Youtube type video "casting" is what you are looking for?