@mitu - I've done some more digging. The GameStick doesn't seem to be recognized properly by the evdev system. Found some fun log messages via dmesg:
[ 15.328485] hid-generic 0005:0F0D:1011.0003: unknown main item tag 0x0 [ 15.328963] input: GameStick Controller as /devices/platform/soc/3f201000.uart/tty/ttyAMA0/hci0/hci0:11/0005:0F0D:1011.0003/input/input2 [ 15.330713] hid-generic 0005:0F0D:1011.0003: input.hidraw2: BLUETOOTH HID v7.07 Keyboard [GameStick Controller] on b8:27:eb:03:bd:7fIt appears that the "unknown main item tag" error (which, googling around, seems to be a bug), is causing the controller to be detected by evdev as a "Keyboard". Which, obviously, doesn't work so hot for controller stuff, since the various buttons don't seem to map to anything ES's controller setup recognizes as a button or axis.
I'm going to see if there's any kind of config option or something I can pass to allow this to work...