You are absolutely correct on all points, and my typo saying LEDS instead of LED has really confused everyone, I am sorry about thatI read it as all LEDs off meaning the cathodes are not connected to ground until button is pressed.
Button press freezes the count for 5 seconds with the one LED lit.
Repeat button press sometime later to reveal which # LED is now lit.
The TS mentioned it was for a game. Maybe whatever number LED is lit means that's how many spaces you move on a board game or maybe you are to try and guess which number LED will light when the button is pressed.
I don't see the point for #2, all LEDs on


