Check out this article. It's kind of old, but still quite relevant - I used it to build my own Stripe integration plugin for Wordpress.
Note that including the line:
require_once('vendor/autoload.php');
should load the Stripe libraries for you. Depending on how you have your plugin folders set up, the plugin might not be finding the autoload.php file. It's best to set a base directory in your plugin's primary php file as such:
if ( ! defined( 'PLUGINNAME_BASE_DIR' ))
define( 'PLUGINNAME_BASE_DIR', dirname( __FILE__ ) );
Then, your require statement would look like:
require_once( PLUGINNAME_BASE_DIR . '/vendor/autoload.php' );
Even better, put the Stripe library in a /lib folder in your plugin, so your include would be:
require_once( PLUGINNAME_BASE_DIR . '/lib/stripe-php/vendor/autoload.php' );
There is also an init.phpinit.php file in the library that does the same thing and is what I used since I didn't use Composer to pull it in. You can use this by downloading the source for the stripe-php library and putting the raw source in your plugin directory inside a /lib directory.
require_once( PLUGINNAME_BASE_DIR . '/lib/stripe-php/init.php' );