The Square unit uses the headphone jack. It exchanges data through tones being sent back and forth over the speaker and microphone pins.

Since there are no unpublished APIs being used, no App Store terms are being violated.

You can do a lot when you can send and receive serial data over a port. Millions upon millions of devices that you never see or know about communicate in this very manner.

like what devices? not doubting, just curious

Your home is filled with microprocessors that talk to each other over two-wire serial protocols. Your oven probably has a control panel that talks over I2C or some other serial protocol to a control module.

That credit card terminal on the shop counter has a modem that talks to another computer the old-fashioned way: frequency-keyed tones over a phone line.

Your car has more chips than you think, all talking over a shared serial bus like CAN or DBUS (not the desktop protocol, the Bosch one).

That touchscreen on your smart phone communicates with the host processor over a serial protocol.

In the embedded systems world it's cheaper and easier to use these ancient protocols than to try and install ethernet lines and TCP/IP stacks...just so that your oven can start a bake cycle.