I don't know how the screenshot service that you linked to works, but it probably uses a headless browser like PhantomJS to render the page and then to capture a screen shot. PhantomJS uses WebKit, the rendering engine that is used by Safari and the basis of the Chrome rendering engine.
Your site uses parallax scrolling which might make this task difficult.
Regardless, to capture a screenshot of an entire webpage, a good solution is to use an extension or add-on to your browser. Here are links for screenshot extensions for several good browsers: