To have the subscribe/newsletter widget like on the demo page, please install this plugin: https://wordpress.org/plugins/mailchimp-for-wp/
After installing the plugin, configure your subscription form following below steps:
- Go to MailChimp for WP > Forms
- Select at least one MailChimp list to subscribe people to.
- (Optional) Add more fields to your form using the add MailChimp field dropdown.
Save the configuration and navigate to Appearance -> Widgets and drop the widget Mailchimp Sign-up Form to your desired sidebar.