There is no RestfulService class in SS4 (it was removed as you can use an external dependancy like Guzzle instead), so cURL is probably not required for a basic SilverStripe installation.
Edit: I only ready the body of the post, after reading the title I’m not sure I understand your problem. Can you post a screenshot of what you’re talking about? (Linking to http://localhost/ URLs doesn’t help us much as we can’t access your local environment.)