You are running into problems with some performance optimizations in the code for handling bit banging SPI. Galileo has hardware SPI so this isn't needed. I added preprocessor directives to skip the code. I have attached my TFT folder to this message. I have no way to test it as I don't have your LCD but it should be a good start. I have a different LCD but I made similar changes to get it to work. If it does work, I expect it to run really slow. You will see it plot a pixel at a time. There are some optimizations that can be done to speed up the SPI communication. I didn't do this because it is important to get something working first.
I added ifdefs around the atmel specific header. I see that mikalhart came up with a better solution. He has a replacement header file at: https://github.com/mikalhart/galileo-Pgmspace.h This is a better over-all solution although the ifdefs will work.
