How do I say to Twig where to look for the template files?
What you found is the class used from Twig to load the template files from the file system, but what Drupal uses is its own class derived from that,  Drupal\Core\Template\Loader\FileSystemLoader, which is the default class implementing the twig.loader.filesystem service. Its only purpose is adding a namespace for each theme and module enabled from a Drupal site, so that is possible to reference a template file as @block/block.html.twig.

For how I understand it, replacing the class implementing that service with a class derived from the default implementation, you could be able to reference 
a template in a different directory with, for example, @external_directory/template.html.twig.

See  FilesystemLoader::__construct() for how Drupal adds new namespaces, and Altering existing services, providing dynamic services for how to alter that service to use a different class.