In the article you have mentioned, Amila has explained about how to define a REST service on ESB.
CURL is a way of testing the REST APIs. Another way to access the REST APIs is using a web browser.
Any client program which can send the REST requests (GET, POST, DELETE, UPDATE) can access your defined student APIs without any issue. You need to host your server in a URL and give the accessibility to that URL for the outsider world. API Manager is such a product you can use to publish your API to outsider world. But it is not necessary.
If you want to expose these as SOAP services for a SOAP client, you can do that as well. For that you can use the following link.
http://docs.wso2.org/wiki/display/ESB460/Using+REST+with+a+Proxy+Service
Hope this help you to figure out your issue.