Is activating via PowerShell also dangerous, even though the computer is essentially just for gaming?
It depends. Do you understand what this Powershell script did to your gaming computer?
Let's look at the extremes.
A) The script doesn't contain anything nasty. You're good. Do we know this? Not likely.
B) The script hid some malware on your gaming computer which can load more sophisticated malware which potentially could infect other devices in your local network. The malware infection could therefore potentially reach a device where you operate your crypto wallets with. You don't do your crypto stuff on your gaming device, do you? I hope not.
Your gaming computer likely needs to be online, so do most of your other devices in your local network. If you don't isolate your gaming computer from your other local network devices the malware could potentially spread as outlined above.
Is it likely that you have the network equipment to securely isolate your gaming device in a separate VLAN? I don't think so (educated guess).
Can your accounts that you use on your gaming device be compromised. Yeah, could be, if it got infected. Do you use any of your more important email accounts on that gaming device? If yes, it's getting worse if the gaming computer is potentially infected.
Can you know if it's clean or not. Not very likely!