To be clear, I am only talking about the interpretation of the regulation, not my own considerations.

The article made it sound like IP addresses are always personal data. My point is that, if I run a website and keep generic nginx log files, is it really personable data with regards to my website?

Yes, the ISP can link that IP address back to a person, but if that person came to me as the website administrator and asked for all data held for that person, I would actually not be able to make the connection.