Note: this is useful if you want to have a prerendered videos play as a backdrop during cutscenes or during normal gameplay.

There are a couple of ways to do this:

  1. AC allows for the playback of movie files with the Engine: Play movie clip Action.  On desktop platforms, you have an additional option to play a movie file as a texture - meaning you can have a movie play on a square plane and position it in front of both the camera and the player.
  2. If you imported each frame of the sequence as a separate image file into Unity, you could combine them into a single animated sprite within Unity (using Unity's built-in animation tools).  This might give way to larger file-sizes, but may be more flexible if you want to easily transition from one animation to another

[Original tip provided by ChrisIceBox]