Too late to edit my comment, but it looks like I didn't quite understand how Apple Pay works either. After a little more research on both of them, here's the gist of it: Apple Pay and Google Pay both create a "Device Account Number" for your card, and this number never changes. When you tap your phone to pay, it generates a one-time cryptogram for the transaction which will always be unique. I was under the impression that merchants only get the cryptogram, but that's not the case – merchants get both the cryptogram and the DAN during the purchase.

The problem is, since the DAN is a stable number that never changes per card, they can save it and use it to recognize you across visits. That's how stores can tie Apple Pay/Google Pay transactions to loyalty programs without scanning a separate card. The DAN doesn't differentiate between online/in-app purchases and physical purchases either, though the number is different between devices (i.e. use phone to pay in-store, use computer or tablet to shop for groceries). But realistically, Apple Pay/Google Pay would only marginally improve the privacy in the Walmart scenario, which is a bummer.