Your hardware probably doesn't match the requirements properly. Check the system requirements on Steam and compare them to your own. (If you don't know your system specs, click Run in the Start Menu and launch "dxdiag". This will tell you everything you need to know.)

Once you know your computer's specs, you might still be able to run the game. I suggest asking on the Steam forums about a workaround (make sure you provide your computer information). My computer sucks and I managed to force Portal 2 to run on it, so it's possible some tweaks could get Shogun 2 to run for you.

My pc seems to more than satisfy all the requirements. I'm starting to wonder if it's just a Steam thing, because the Space Marine demo doesn't work either.

I found a possible fix afterall.

Cool, try that.

Sometimes your hardware IS sufficient, but some small difference keeps it from working. For example, even if a GPU is the same type on desktop and mobile, there might be slight differences between the few that cause one to be incompatible. Those kinds of issues should be easy to fix, though.