Right, so the gist is your code; from your description I thought it was someone else’s code you read for inspiration.
Your woostripe.php file, which loads your gateway class, bails out before loading the gateway class:
// bail on constructor if gateway class isn't loaded!
if (!class_exists('WooStripe_Gateway')) return;
// ...
// why are you attempting to load WooCommerce's classes? Don't!
include_once(dirname(plugin_basename('woocommerce.php')) . 'classese/abstracts/abstract-wc-payment-gateway.php');
// never gets here to load this class, you've already left this function...
include_once(dirname(plugin_basename(__FILE__)) . 'classes/WooStripe_Gateway.php');
Remove the include statement for WooCommerce’s class, that’s WooCommerce’s job not yours. Then move your WooStripe_Gateway include to the top of woocommerce_gateway_init() before the test to see if it exists. That class cannot exist until it is loaded.