What causes the “Twig_Environment not found” error?

Isn't third_party libraries loaded through the $autoload['packages'] array? Autoloading libraries only looks for the /application/libraries/* directory, you use the /application/third_party/* directory for this..

Edit:
My mistake, reading to fast on this topic.  
You use the correct folder according to the documentation

Do you encounter the same issue when you install the required environment through composer?
Based on the error you give i think the Twig_Environment isn't loaded correctly.

I have not tried with Composer and I would rather not. I want the deployment process to be very simple.

Have a look at the GitHub repo. 

Thanks!