The article is misleading. It talks about how it can be used to "identify someone." And with all the talk about privacy, it implies the identification of an individual.
But, reading through it closely, they aren't talking about identifying a specific someone; the information isn't enough to say Not_Wiggins made these purchases.
Instead, it focuses on identifying characteristics of purchasers and then extending it to see what other behavior purchasers in those groups would make.
In the article example, they talked about someone making a purchase at both a bakery and a restaurant within a short time period. Finding that they had one such instance, named him Scott, then looked to see what other behaviors "Scott" had. By extending that logic, they are saying "look at the group of people who typically shop at a bakery and a restaurant... then you know those people are typically also interested in shoes."
The example is a bit silly, but that's what they're saying.
They're talking about documenting patterns of behavior on purchasing decisions.
This article really isn't about loss of anonymity. It is about using anonymized credit card transactions to develop definitions of "user groups" and predicting their shared behavior pattern.
To me, it seems more like the equivalent of last.fm... tell us what music you like, we'll compare it against what others who also have the same "likes" have said, and give you options for things that might fit your tastes.
In this instance, it is: tell us what purchases you've made, we'll compare it against similar purchases that others have made, and we can predict what other purchases you might want/like that you haven't made yet.