I use the classic magazine#2 layout for my pages e.g. sputniq.net/politik. But in the Post Grid are only the featured pics are show. No Headline, no excerpt text, no link like on your demo site.
Have I edit something?
Go to Appearance > Theme Options > Content > Post Grids and select to show the items. These should all be set to show by default, so most likely you’ve accidentally turned these off at some point when going through the theme options.