The black bars are nothing more than the cleared back buffer. The video is simply being centered and played between these two bars. This effect is known as Letterboxing. The only thing you need to do in DirectX is simply render the video accordingly (vertically aligned). That being said, a lot of the time these bars are shown because aspect ratio of the video is different than the game.
You do not change the resolution of the game while it's playing (at least, this is not a common approach). Rather, you calculate if the video aspect ratio matches the current aspect ratio, and if so, simply play it. If not, you can vertically center it.
** Some games are known to use letter boxing regardless to indiciate a "scene". You may choose to do this, too.
This post by Nick Gravelyn has more info.