`Drupal\DrupalExtension` extension file or class could not be located
The Drupal Extension requires no modules, only composer installation.
Execute:
composer require drupal/drupal-extension='~3.0'
See the docs for other setup information: https://github.com/jhedstrom/drupalextension/blob/master/README.md
Update
to install the latest version just use
composer require drupal/drupal-extension

[version 3 is kind of outdated and in this time latest version is 4.1]