Take a look at the implementation of the Game class in MonoGame.
https://github.com/mono/MonoGame/blob/develop/MonoGame.Framework/Game.cs
In the constructor it creates a GameServiceContainer and then uses it in the GraphicsDevice getter to get an IGraphicsDeviceService.
To make matters more difficult the GraphicsDeviceManager takes a Game class in it's constructor and adds itself as a service to the service container creating a tight coupling between these two classes.
https://github.com/mono/MonoGame/blob/develop/MonoGame.Framework/GraphicsDeviceManager.cs
This is not particularly good design for unit testing but it's not the fault of the MonoGame team because they are just re-implementing the behavior of Microsoft XNA.
I suspect your issue is that your GameLoop class depends on having a valid Game class already constructed which in turn uses the service container internally.
My suggestion is to design your own code so that it can be unit tested and try to decouple it from rendering code in the same spirit you would separate the view from a view model. At best, you might be able to use screenshot tests to confirm that things render correctly if you're really keen.