denete

For what it is worth, the success response in line 17 of the snippet you provided what should allow the form to proceed as normal.

You are correct. In the head of the page is…
<script src='https://www.google.com/recaptcha/api.js'></script>

Added to wp-content/plugins/give/includes/forms/template.php line 1135…
<div id="give-recaptcha-element" class="g-recaptcha" data-sitekey="xxx_sitekey_xxx" style="margin-bottom:1em"></div>

Added to custom JS for the page…

jQuery(document).on('give_gateway_loaded', function() {
    grecaptcha.render('give-recaptcha-element', {
        'sitekey' : xxx_sitekey_xxx'
    });
});

Turns out that it was an issue with me using grunt-compress to compress my theme directory.

Sorry for any confusion.

Closing as resolved.