There isn't a SOAP API to retrieve the Enterprise WSDL. That would be a bit circular, as the Enterprise WSDL itself is for the SOAP API.
The CURL instructions that you linked to are about as good as you are going to get. Basically, you need to make a GET request to
/soap/wsdl.jsp?type=*. The request needs to be authenticated with a valid SessionId via the sid cookie. You will be more or less screen scraping the Enterprise WSDL from Salesforce.
One suggestion - if you are expecting sufficient changes to the Enterprise WSDL that you will need to automate handling those changes you may be better served by the Partner WSDL. The partner WSDL is dynamic and will adjust automatically to any changes in the target orgs Metadata.