Looking closely at your photos, the physics is puzzling.
1. it is not your eyes, since the camera taking the pictures sees it too
2. it is not a head lamp, since then there would be reflection not a brightness from the screen
3. sophisticated software could do it but it would require eye tracking and some kind of screen overlay
- and I wouldn't know why anyone would go to that effort, since it would be terribly annoying
- you assured us that the webcam is off
4. the screen could be fried, but the fried part would not move
5. it is not the brightness level since the indicator that's on your screen is high in all pictures
6. the following questions come to mind, but I have no idea how the answers would help
- When you move away from the laptop is there any light coming from the screen or does it go black?
- What happens when you turn up the ambient light or lower it?
- What happens when another person looks at the screen?
- What is your ambient temperature? Very hot? Very cold?
7. it is a real screen - you're showing the Forum in real time
8. if I tried to create this effect, I would not know how
Conclusion: probably as
@udg said
I have had many HP laptops in my life but never one with a "HP SureView Integrated Privacy Display"
But I can see situations where it would be very useful.
I hope this is the case for you and that you can turn it off.