When using the Gmail integration, you can add existing Vidyard videos but not players as part of your email.
When you add a video from your library in Gmail, it automatically creates a new player. This new player will collect the analytics of the viewer whose vyemail string is attached to the email. Here is an example how to Vidyard identifies viewers using the vyemail string.
You can replicate a player's playlist by selecting the same videos as the original player has.