You can create a system overlay and play the video on it. Create a service and add this code:
@Override
public void onCreate() {
super.onCreate();
WindowManager.LayoutParams params = new WindowManager.LayoutParams(
WindowManager.LayoutParams.TYPE_SYSTEM_OVERLAY,
WindowManager.LayoutParams.FLAG_WATCH_OUTSIDE_TOUCH
|WindowManager.LayoutParams.FLAG_DISMISS_KEYGUARD,
PixelFormat.TRANSLUCENT);
params.gravity = Gravity.RIGHT | Gravity.TOP;
WindowManager wm = (WindowManager) getSystemService(WINDOW_SERVICE);
wm.addView(yourView, params);
}
Remember to add SYSTEM_ALERT_WINDOWpermission inside the manifest.
EDIT. TYPE_SYSTEM_ALERT TYPE_SYSTEM_ERROR TYPE_SYSTEM_OVERLAY.