I've never personally done it, so done a quick google for you as I didn't think what you were doing was right.
I found this on stack overflow:
Which then lead me to the below site from one of the answers:
Open the "Game1.cs" file at the above github site and see how they are playing the video.
In the loadContent put:
video = Content.Load<Video> ("sintel_trailer");
videoPlayer = new Microsoft.Xna.Framework.Media.VideoPlayer();
playVideo = true;
And in the update method put:
if (videoPlayer.State == MediaState.Stopped)
playVideo = false;
Note: The stackoverflow question is now 5 years old so it might not work 100%, if not I'm sure one of the more regular monogame users will reply and correct me.
Hope this helps.