I had a little moment in a short break @ work and did a little debugging session.
I found the problem and will push the fix soon.
The problem was that the VideoPlayer creates a video cache (Texture2D) to play the video. For that it needs to get the current GraphicsDevice by accessing the current Game instance, but this is not possible in MonoGame.Forms, because it doesn't rely on a Game instance.
I fix this issue by creating a new ctor for the VideoPlayer where it's possible to give the GraphicsDevice from the GraphicsDeviceControl of your custom MonoGameControl by overloading it.
I already tested this and it properly plays the video in MonoGame.Forms!
Also thanks that you want to support the project with a donation, this is always appreciated. I will create a PayPal donation button on the GitHub page of the MonoGame.Forms project soon (together with the new update).
I will inform you about the new update here and in the showcase thread.
Thanks for your support!
I think I can manage to push this new update to GitHub and NuGet this evening or tommorow. I hope this is fine.