Download the RetroPie image to a Windows PC. You will need to uncompress the .gz file using 7-zip. Then use Win32diskimager to burn the image to an SD card.
Don't be alarmed when you power up the PiCade/Raspberry Pi for the first time and nothing shows up on the screen. Because the Pi looks for an HDMI source before it powers up the USB ports, the screen will not be detected. Remember, the screen gets power from the USB port and if it has no power it looks like it is off or not present.
You can force the Pi to output to HDMI by editing the /boot/config.txt file (you can do this by popping the SD card into a a separate Raspberry Pi). Edit the /boot/config.txt by typing sudo nano /boot/config.txt into the terminal. To access the terminal just hit the F4 key on your keyboard. Add the line hdmi_force_hotplug=1 to the bottom of the config file, save, and then reboot your Picade to enable the change.