I don't know if this is a game error or Steam error, but you can reset Steam and see how it goes
If you were to go to Steam support, they would probably tell you to do this first, so you might as well try it.
This a way of reinstalling Steam
WITHOUT losing all your games, and userdata (saved games)
1/ Close Steam
2/ Go to your steam install folder, and delete everything
except the following 3 applications or folders
Steam.exe
Steamapps folder
Userdata folder
3/ Once you have done this, run that Steam.exe that you didn't delete.
Steam will now fix it's files and services, a kind of Steam 'reset'
Now try your game again and hope it works
EDIT: Before start you might want to make sure that you have your username and password available to hand. If you use Steam Guard, then temporarily disable it, otherwise you might have to wait for an email with a security code from Steam, before you can log in again. This is just in case your PC is seen as a new computer by Steam.
Run Steam > Steam Menu > Settings > Manage Steam Guard Account Security > Disable
Once you have reset Steam and logged in, you can go back and switch it on again.