IP addresses are subject to GDPR, but that just means that you have to have either a legitimate business need for keeping them or to have the user's consent to keep them and you need to disclose to the user that you are keeping them and for how long.
You probably do have a legitimate need to keep IP address logs for some period of time to allow troubleshooting and possibly for a longer period of time to allow for fraud detection. As long as you are disclosing to the user that you are collecting that information and are abiding by the retention period that you are disclosing to users, then you will be allowed to collect logs of IP addresses.
The classification of data of personal data is likely beyond dispute but you are then under obligations on how you actually make use of that data.
Entities should have in place relevant protective measures to ensure that if you have only collected data for a limited purpose, it should not be used for purposes beyond that.
I’m not familiar with the referenced Nintendo case, but mens rea is usually only considered in criminal cases. Unless you’re prosecuting someone for illegally downloading copyrighted material or some such thing, intent wouldn’t be considered (it can increase liability in civil cases, though).
By my reading, information becomes personal —and therefore subject to GDPR— when it can be used to identify people. If you've got login timestamps, IP addresses and user records, for legitimate reasons, any other logging that includes IPs is tainted because it takes anybody with that data two minutes to munge them together.
Intent, and actual business use-case play second fiddle to the worst-case, or "what could that data be used for?".