Back to HP to correct or refund. You make one mistake and that's not yelping the moment you found it broken.
Maybe the full model number was in your very nice long post but without it I can't see if folk found fixes or if there's an issue with the games and that model laptop.
What else I run into are folk that format the machine and can't get the GPU to engage. Again, the same answer. Install the OS as supplied by HP.