I'm gonna be short and sweet about this. This ain't gonna be pretty....
Go to your Amnesia.app and right-click, choose "Show Package Contents".
Navigate to Contents > Resources.
Once in the Resources folder, go to the terminal window and type "cd " (include the space, no quotes)
At the top of the finder window you can click and hold the folder icon in the titlebar, then drag the folder icon into the terminal window so it will place the path to the Resources folder in front of the "cd ". Hit Return.
In the Resources folder you'll see yet another Amnesia.app with the icon and everything. Right-click this one and choose "show package contents".
Navigate to Contents > MacOS
Drag the single file "Amnesia" into the Terminal window and hit Return.
Amnesia should now open (it may ask for a serial if this is the first run).
I've read somewhere that the cause of the problem is that the Amnesia game is trying to run using the wrong directory, hence why it can't find and load it's config files. This trick also works very similarly with the Penumbra games for Mac as well except for Black Plague there's a BlackPlague file instead of another .app.
By no means is this a permanent fix but at least you can run the game on Mavericks!