This article seems to bury the main point:

we're currently getting about 30M hits a month on our API

If you're getting a million API requests a day, you can probably handle that load with a single machine. Indeed, it looks like they are using just one load balancer machine, one app server, and one db server. I'm not sure why the load balancer is even necessary. It's cool to hear this story, readers should just keep in mind that this is not really a "web scale" deployment.