I *think* I solved this while trying to get to sleep last night
The new amnesia is built with a later version of visual studio, which needs dll files that can not be bundled within the game folder. Can you please download the following files and install them and see if this fixes it? (if so this will be bundled with the game and auto-installed in the system. It actually does this already for standalone version, but not on Steam.)
http://pub.thedarkswarm.com/temp/vcredist_x86.exe <-Take this first, install and try the game. If not working then also take this ->
http://pub.thedarkswarm.com/temp/vcredist_x64.exe and install and try the game.