Any particular reason you want to limit yourself to these colors? With the exception of very high restriction consoles like the NES, the palette of an entire game is not usually quite as limited. Instead, each asset has certain restrictions ( most commonly, 16 colors for SNES, with one reserved for transparency in sprites) and the palettes of each can add up to many colors on screen at once.
I'm sure one could make a great looking game with this palette, but that has more to do with art direction, design, and perhaps a little bit of cleverness. Why don't you try doing a mockup for your game using only this palette and we can give you critique on it?