It´s an Android-Feature; not a feature of your app.
I suppose you need to disable the screenshot-feature in android itself. But i believe this only can be done with a rooted device. If so then i dont know how to do that, sorry.
When a Video on Youtube is playing, I can't make Screenshots. It pops up a ToastMessage saying that *the video is protected by DRM.*
If Youtube can, we can
But how?