Felix i've tried the "Rain Demo" exported with Awesomium on my gf's pc and i got the same problem. She's got a 64-Bit system so i think thats the problem. It's running fine on my 32-bit Windows 7 Ultimate.
That make me think (normally I are thinking)
I then use the dependency dll software (the best tool around "dependency walker")
this determine the system not found "awesomium.dll"
then I copy that file in the windows\system32 and then
already fixed is run now (not forgot execute like administrator)
Appear The 64 bit version not search for dll inside the folders?
You try that and tell me is works for you.
For distribuite using a intall tool can make the fix but
is we like to distribuite to the users a game without intallation process then with have a problem in the 64 bit system