The image doesn't really contain enough pieces to compile on Galileo itself. You can either use the cross-compiler toolchain on your PC to compile stuff for Galileo and then copy the binaries over to the board using e.g. SSH, or build an image containing SDK and compile on the board directly.
For the former see the BSP Build Guide, there's a section about building the toolchain, for the latter see e.g. instructions on SergeyK's blog mentioned in some neighbor threads (though he's doing slightly different thing there, building an LSB-compliant, eglibc-based image, which also has SDK tools).
That makes sense; thanks for the help Alex, much appreciated.