Subscribe form works as an e-mail newsletter. To activate such form with an enabled MailChimp service, replace the .rd-mailform class with .mailchimp-mailform and the form's action with MailChimp subscription URL.
To activate the Campaign Monitor service, you need to replace the form’s .rd-mailform class with .campaign-mailform and copy the form's action and the name of the input field from the form generated by Campaign Monitor service.