They'll know a customer's ip address. They can tell which websites customers are going to based on DNS lookups. This circumvents a browser's Do Not Track or disabling of cookies because their is no need to adhere to it. Unless you're a savvy patron who knows networking by manually changing the DNS address, most people will use Google's DNS address. Even then Google can still figure out where you're going by doing some Deep Packet Inspection sampling on traffic passing through their networking gear. By clicking on their terms of service, a patron is basically allowing them to do this, thus giving up more of their info to the Marketing Juggernaut.
I haven't used their wifi service, but I'm assuming you'll need to register for a Google Account in order to use their service. Then they'll probably have some kind of jump point to sell you Google products, like music as you sip your expresso drink. They even made an app that has an auto-login capability. It's supposed to be "convenient" for you so you don't have to open a webpage and click "accept" on their terms of service every single time. However this also means that Google will know every time you walk into a Starbucks and how long you spend time
I don't know how many people use the wifi at a Starbucks location, but I see quite a few people on laptops tapping away on their keyboards dreaming up of the next big startup. I wonder how they would feel if they knew it wouldn't take much for Google to see what they were working on. Well played Google. I'll have a Tall Vanilla Latte please, hold my privacy please.