new-ga-tracking.js

<script>
  (function () {
    var analytics = window.analytics
    if (!analytics) return

    var appInstallButton = document.querySelectorAll('.js-partner-tracking');

    analytics.ready(function () {
      ga('create', 'UA-REDACTED', 'auto', 'appTracker');
      ga('appTracker.send', 'pageview');

      if (appInstallButton.length) {
        appInstallButton.addEventListener('click', ga('appTracker.send', 'event', 'Shopify App Store', 'Get App button', "REDACTED"))
      }
    })
  })();
</script>

appInstallButton.addEventListener('click', ga('appTracker.send', 'event', 'Shopify App Store', 'Get App button', "REDACTED"))

This is where the bug is. addEventListenershould be passed a reference to a function. Right now, it's calling the function immediately.