In this article the author states: "The latter definition is important for developers. It includes things like IP addresses, mobile device IDs, browser fingerprints, RFID tags, MAC addresses, cookies, telemetry, user account IDs, and any other form of system-generated data which identifies a natural person.". This information does NOT automatically qualify as personal data. Information being unique is not the same as personally identifiable. A random cookie sent by the browser is not PII. A cookie stored in conjunction with say an email address could be.
Certain information can be classified as PII if it possible to cross reference it with other stored information to identity a user. For example a European court in a recent ruling stated that a full IP address could be considered PII because an ISP would have a record of IP address and time with a persons name.