So, that’s an interesting point. A provider would need to know where to send traffic to, but the idea is generally that they run services from RAM with minimal logging and associate the port forward with your account ID (or some other sub-account ID). That would prevent them from having to record IP address info, but in truth if a VPN provider says they are no-log you are really just trusting them that they aren’t lying.
Even if they show they are 3rd-party audited, people need to understand that they KNOW when they are going to be audited and the scope of the audit. Its incredibly easy to game that system if you control how its done.
That being said, if you look at it observationally, people who use port-forwarded VPNs do not receive DMCA notices anywhere near the extent that non-VPN users do, and there isn’t any real DMCA notice discrepancy between port-forwarded and non-forwarded VPN services.