This is my site, and even though you're competing with me I'll help ya out.
I'm not using any plugins, it's all standard wordpress template tags and template hierarchy, you can read up on that in the codex. http://codex.wordpress.org/Template_Hierarchy
I started off with the massivepress theme, it's pretty old and had none of the new wordpress features like custom menus, etc so I added in all that.
To make your categories look different you can use category-photos.php (for example) where "photos" is the slug of your category. WordPress will automatically use that template file for the "photos" category. Your default category.php will display the other categories. You can do this for tags and single posts as well.
For the photos section particularly, I'm using do_shortcode(gallery) to display photos with just "the_title".
For the video section, it's same except I use "Vipers Video Quicktags" in combination with the "Video Thumbnails". The latter grabs a screen from the video embed with Viper, and adds it automatically to the post gallery as the featured image.
So it's just a matter using Template Hierarchy to display the content however you want it.
And please find your own unique way of doing it, rather than copying like you did with my Home Page Featured Posts thingy. :D