Hi Rafael,
I had the same need a few months ago and I got video working in Linux with MonoGame 3.5.1 by adding TheoraPlay, Video and VideoPlayer classes as suggested:
Here:
And here:
Then I just had to install libtheora0, convert the videos using ex: VLC and then load the video file with MonoGame.
Those files don’t work with MonoGame 3.6 as they are because some GL functions changed.
If it helps I can upload a working sample of what was working for me…