I'm sorry this has happened to you. It's the downside with AMOLED but to my knowledge, this is the first case that I've seen in this forum. There is one other thread that I know of but his "burn-in" didn't really look like a burn-in.
Regardless of the nature of whatever defect your screens might have, you need to contact the support in your country. I can't comment here if it's within warranty or not. It's up to them to take a look and determine if it will be covered or not.
aabs22can i ask which charger do you use while gaming? Official asus charger or other charger. I play heavy games like PUBG Mobile and my phone reaches 47° C while charging WITH OFFICIAL 18W CHARGER. I tried out oneplus charger and my phone temperature was reaching upto 53° C which might be harmful for the device. i suggest you to not use other charger while gaming to prevent damage.
May be the first case but certainly not going to be the last am afraid, as you said AMOLED and the Burn-In on AMOLED displays are a common thing which I got to know after a simple Google search but it was already too late for me. If not now but eventually alot of users are going to possibly report this sooner or later. ASUS being a lead player in this field should have done their R&D. It's a phone designed for GAMING and they should have thought it through that most of the customers are gonna be GAMERS. If you ask me had I known about AMOLED and its drawbacks I wouldnt have suggested to go with it for any phones designed for GAMING let alone ROG2. Now I have to run behind Service centres if its not known but after-sales service is pathetic here and its heart breaking to imagine my new phone is going to be possibly ripped and hope for it to come back in one piece. Frustrated and Disappointed to be honest. I dont have the privilege of time to spare but will try to reach out to some Service outlets and see how my luck turna out to be. Thanks!