Ah I missed two obvious things. Sure helps to read the spec. 1. .php not .inc 2. Class = Name of file

behat_editor_saucelabs.module

<?php

use Drupal\BehatEditorSauceLabs;


//Later on

composer_manager_register_autoloader();
$check_connection = new Drupal\BehatEditorSauceLabs\BehatEditorSauceLabsWrapper($username, $api_key);

BehatEditorSauceLabsWrapper.inc

//src/Drupal/BehatEditorSauceLabs/BehatEditorSauceLabsWrapper.inc

<?php

namespace Drupal\BehatEditorSauceLabs;

class BehatEditorSauceLabsWrapper {
  
}

composer.json

{
    "require": {
        "instaclick/php-webdriver": "1.0.16"
    },
    "autoload": {
        "psr-0": {
          "Drupal\\BehatEditorSauceLabs\\": "src/"
        }
    }
}