I can share my recent experience of getting a "gaming" laptop with you. I travel for work a lot and recently got a used laptop (HP Omen 7700HQ, 12GB of RAM, 256GB SSD, GTX 1050 ti) for $400. I upgraded the memory to 16GB, and added an Intel 600p 1TB NVMe drive for another $150. Since this is a work laptop I cannot install Steam, but I did install one of my recent favorite Age of Empires Definitive Edition (a reboot). I can't tell you how much fun I have had for the last couple of weeks. You see, when I am home, I work and spend time with family. Only when I am on the road, I have some down time. So now instead of watching movies, I can play a game of two.
The only concern is bulk. My laptop with power bank currently weighs 5lbs. That would be the max for me as I don't want to lug a heavy laptop with power bank around for long walks. If you up for the challenge, a gaming laptop (no eGPU, that is too much bulk) would be the way to go. Does the heat throttle the performance? Not for me, as my game is not that intensive, but I can hear the fans whirling.
So, is this a Best Buy warranty replacement? How much credit do you have? Depend on the game, the budget, the bulk you are willing to carry. I would suggest at least a 1060 or an RTX 2060 to be a good trade off of heat, bulk, and budget.