There is little special about mobile payments. The transactions are still processed through credit card networks. They still use credit cards.
Square is just a re-seller of processor services. It's on the hunt for merchant accounts. And it bagged a big one with Starbucks.
I'm making a guess here that Starbucks (SBUX) isn't taking the standard Square deal, a 2.75% discount on charges. This replaces the variable discount and swipe fees offered by most banks, and it's a deal that has brought Square a lot of small merchants. But Starbucks' credit is good enough that they can get a better deal than that. I'm sure they did.
The companies this really challenges are current merchant processors. Square isn't a technology company. It's a bank. It's betting that it can make money on the 2.75% discount and a month's float, instead of variable discounts and swipe fees offered through standard processors working with MasterCard (MA) and Visa (V). The technology itself is nothing special - a small swiper to read card numbers and transaction details and some standard encryption. I assume they're PCI compliant.
In addition to the processing deal, Starbucks gets two other valuable things in this deal. It gets customer data, and probably gets it more quickly than with a common Visa processor. It can use this data to identify patterns, to reward frequent customers, to push deals and increase sell-through and customer loyalty. It could do those things before but now it's faster, and the data flow is explicitly protected.
Then there's the equity. Starbucks is part of a $50 million round of financing, and this is easily a multi-billion dollar company within a very short time, in part because of this deal. So kudos to Starbucks.
But the world isn't changing. Transaction processing is getting more competitive. The race to get merchants is getting more competitive, and some re-sellers may be pressed to the wall in time by this. That industry was already consolidating - most banks and credit unions are handling their credit card operations through one of several major institutions.
It's interesting, but until someone in the mobile space starts creating its own credit card accounts, and processing its own transactions front-to-back, issuing its own bills or taking money from prepaid online accounts, it's evolution and not revolution.