Interesting. Starbucks is obviously not going to use the error-prone dongles. I suspect Square will provide some sort of custom "Pay With Square" solution, perhaps tied into Starbucks' existing point-of-sale system. Any way you look at it, it's a huge deal for Square, Starbucks is absolutely the best venue for Square and likely the key building block to really push out a new checkout experience such as "Pay With Square".
I am assuming at the volume in question they'll just retrofit whatever software to use the card readers Starbucks currently uses. They're pretty well built.