Hard to say what's going on there, because the URLs don't give anything away. However, I'd say that the pages that show as lists of posts are category lists. If that's the case, it's just a case of creating the categories, adding some posts associated with those categories and then adding the categories to your Primary Navigation menu.
The 'Home' page looks like a category list as well, because it's not showing things that crop up in other lists as far as I can see.
One thing that would worry me would be how to make a category list the front page. There's no problem about making a category list and calling it 'Home', but that's not the same as having it appear as the 'index' file. That's not a problem on the demo, because there is no 'index' file. The 'index' file shows at http://themeforest.net/ and is a 'static' page, which is easy to do.
HTH
PAE