To clarify, I’m assuming not talking about Bink media player.
Media Player doesn’t seem to automatically open anything, which means it won’t start when you play the level, and what you see is the freeze frame from when you were looking at the player in the editor.
The media player is tied to the texture, but it’s not tied to any particular source. When you view it in the editor, you see available sources, but none are explicitly tied to the player.
If you check “play on open” in the media player, you still need to open the source.
You can do this in a blueprint that resides in the level, or the level blueprint.