How does this work?

You can't screenshot in Netflix and Amazon Prime. Whenever you try, either a black picture comes out on the PC, or the cell phone says that the manufacturer does not allow it.

I can understand how it is done on my cell phone, but on a PC?

How does this technique work?

So with me screenshots and films go without problems

Called Digital Rights Management (DRM)

With Windows, I think mostly Microsoft's PlayReady DRM is used to play back protected content. But there are also a few others. Apple's is e.g. Fair play
If you want to learn more about it you will find plenty of information below.

Have now tried with D3DGear, Bandicam, OBS and Win10's own tool (Wintaste + G) to record with Netflix (Grindelwald) and worked with everyone.