The log doesn't really give anything to indicate a crash. Try running Amnesia in a terminal and see if there are any error messages in there. The command is:
From the directory you installed Amnesia in.
(mine is 64bit version hence the "bin64" extension. If you run 32bit it's probably "bin" or "bin32").
Sounds like you've come from Windows, so I'm not sure how much Linux you know as far as command line stuff is concerned. I apologise in advance if this is a bit condescending for you
cd = change directory
My Amnesia install is in a custom Games directory on my system so the command for me is: cd Games/Amnesia
ls = list directory contents (same as "dir". You can even use "dir" if you want)
./ = execute prefix. A lot of the time you need this prefix to execute the binary file
./
name_of_binary
Running from the terminal is a great way to find out what is going on. Even if you don't understand the error you can copy it and paste it into the forum or google and get some help. It's very rare for a terminal execution to give no feedback at all.
Hope this helps
BTW what distro are you using?