Yeah, like Ferret said, you should switch your render types.
Normally, if I'm streaming a video or recording on my laptop and I'm using something that's full screen, it'll just record a black screen.
Direct3D is the render system that doesn't have the game full screen (although I've seen it be full screen for certain computers, but even then you can change that when you're selecting the rendering system.)
Although, I can't say your screenshots you have already taken will not just be a black screen, I think those will still stay the same sadly. When you test it out, you should take a screenshot and check if that's changed at all.
