There's a typo on line 27 of wp-custom-login-logo.php that reads:
$cssPath = get_bloginfo('url')."/wp-content/plugins/wp-costum-login-logo/wp-custom-login-logo.css";
$cssPath = get_bloginfo('url')."/wp-content/plugins/wp-custom-login-logo/wp-custom-login-logo.css";
It couldn't possibly be pulling in that CSS file unless you named the plugin's directory incorrectly to match the typo. Fortunately, the plugin unzips to that misspelled name, so it does actually work.