Hi there everyone.
Same problem... slightly different solution for me. Used the Arduino as ISP, connected to ICSP terminals as per above, uploaded a sketch as above, which worked. Then tried to upload a sketch from the Arduino IDE... nope. Long story short, I found the following method to work:
(This tutorial roughly follows this tutorial from Arduino http://arduino.cc/en/Tutorial/ArduinoISP)
First:
I'm not responsible for bricked robots, broken hearts, unfulfilled sexual partners, thermonuclear war, etc. Please do some research before you dive in. Guidance only 
Okay, here goes.
As mentioned above, before you upload ArduinoISP to your device that's going to be doing the programming, change the following line.
#define RESET SS
to
#define RESET 10
Upload the code, connect the terminals in the way shown above.
REMOVE THE TFT SCREEN FROM THE ROBOT!
As mentioned here http://arduino.cc/en/Main/Robot
Control Board SPI: ...if you want to flash the processor using an external programmer, you need to disconnect the screen first.
In your Arduino IDE -> Tools menu, select the board as Arduino Robot Control, the programmer as 'Arduino as ISP' and the COM port as the one with your programmer device on it.
Select 'Burn Bootloader', then let it do its thing. Wait until it finishes, then plug your screen back in, upload a sketch and you should be away.
Hopefully this helped some people. Thanks to Noppe for the tutorial.