I'm taking a look at the free cloud and it seems that there is no way to setup a rule with an execute-script action.
Is it possible to create a similar rule in an Alfresco Cloud instance? Is there a difference in terms of customization between Standard and Enterprise version of the Alfresco Cloud?
As you've no doubt figured out by now running code directly on the Alfresco in the cloud instance (like through server-side JavaScript) is not supported. There are no customizations of any kind that are supported. Rules are supported but the actions are limited to copy, move, and transform.
Depending on exactly what you are trying to do you may be able to get by with the Alfresco API. You can learn more about that <a href="https://www.alfresco.com/develop/cloud">here</a>.