Yes, of course it is personally identifying information. It provides identifying information about a person, so why on earth might it be considered otherwise?
Consider a shopkeeper in a small town saying "I think I shall invest in [very unpopular company] when I get home tonight." His customer says "if you do, I will never shop here again!" That night, the customer sees that another investor appears on the company's map for that zipcode.
Would you consider it unreasonable of the customer to stop shopping at that store? Would you consider it unreasonable of others, on hearing this tale, to also stop shopping there? Remember, small town, there probably weren't any investors at all from there before.
Would you consider it reasonable of the shopkeeper to then sue the company for leaking his private investment information and hence causing damage to his business?
So the potential number of zipcodes where the combination of [is a user of that webside's service] and [lives in that zipcode] and [when they started investing] will be uniquely identifying is obviously pretty huge.
But it's worse than that.
The following zipcodes have a population of exactly one person: 05141, 67843, 88264, 98222, 99790. There are over a hundred zipcodes with populations under 10. 11109 has an area of just two city blocks. If you live in 38639 you are also black. If you live in 02562 you are white (better than 99% probability for both). If you live in Beverly Hills 90210, you are rich and everyone knows it. If you live in 90209, you are still rich, but likely have a chip on your shoulder about your zipcode being less famous.
There are a little under 8 billion of us. That means that we need only "33 bits of entropy" -- that is, 33 yes/no questions which slice the population roughly in half, like "are you male", "do you live outside China/India", etc -- to identify any individual. A zipcode provides between 16 bits of information (the two most populous zipcodes have over 110,000 people in) and the full 33 (those 6 zipcodes above). That is to say, a zipcode alone is at least half the information needed to uniquely identify anybody.
[Edit: and of course, in the US, businesses are persons. Many, MANY companies with a technical population of zero have their own zipcodes. If that company invests in another company, they may well NOT like that information being put up publicly.]
[Edit2: Zip codes are explicitly called out as PII by Massachusetts (https://casetext.com/case/tyler-v-michaels-stores) and California (http://scocal.stanford.edu/opinion/pineda-v-williams-sonoma-33947).]