Sound designer/Game Developer based in South Yorkshire, UK
took a while for me to find it. sharing here in case anyone else has similar issue and somehow their search takes them here.. (as long as your device has SD card, anyway...)
first, if you haven't already, get the android sdk (or adb through some other method)..
connect android device with usb debugging enabled (wait for drivers to install if not already done).
only have 1 android device connected for -d to work later on.
navigate in command window to location of adb. (start menu/run/cmd, then go to C:\adt-bundle-windows-x86-20130219\sdk\platform-tools or wherever..)
adb -d shell
(should connect, no error messages)
cat /data/data/com.square_enix.android_googleplay.FFIII_GP/files/save.bin > /sdcard/save.bin
and that's it! it's now on your sd card, in the root. putting it back may be more of an issue without rooting, but at least you have it!! :)