They also only implement serial sending (so the Arduino receives) so far, although they mention the next step would be to build the other side of the connection.

An Android* phone or tablet running Android and has Bluetooth. Connect your Intel® Edison board to a Wi-Fi* network, see Get started with Intel® Edison technology.

Well tech tinkerer Joe Desbonnet has whipped up what he dubs "poor man's NFC" using an Arduino, some magnet wire, and any compass-equipped Android smartphone (which is almost all of them).