1. this is old news. WU has classified IP as PII for a long time now.
2. Yes - it is exactly like your phone number. Given your phone number, I stand a very good chance of figuring out who you are - thus it is personally identifying.
The reason that this is a bad thing to store is that I can get a court order to request all the search records from Yahoo that were made from your IP address - thus showing that you did indeed search for 'male escorts NYC'.
Having it noted as PII means that nobody can store it (in search logs for example) without your express permission, and thus if it ain't logged, the search query can't be associated with your good name.