I did test the example on my board and I have the same messy display as you. I also tried an example project for the STM32F746G-DISCO and it works fine.
Look like the code for the STM32F7508-DISCO is not working due the small internal flash (64Kb) and the size of the image to display on the LCD. I think they wanted to solve that by putting the application on the external Quad SPI flash memory (16Mb). I’m not expert on this subject, but perhaps their is some synchronization/clock configuration issues to access on this memory.
Sorry not being able to help you more.
Maybe you could find information on ST forum.