The demo for that board was written on one of the original hardware versions. I believe the OLED display (or the controller thereof) has been changed several times since then - so it might just be a case of grabbing the latest version of the Luminary/TI display driver from their StellarisWare package.
I know it is a different board, but if you search for the term “Note for LM3S2965 and LM3S6965 users” on the following page, you will see that, for that board at least, the name of the driver file changed too. The same might be the case for your board.
I think it would be best at this point if I switch gears and start working on the boards that are more suitable to our final product, the LM3S8962 & the LM3S9D92.
I hope these don’t exhibit this same behavior or I’ll have to revisit this problem.