The format of what you download depends on the type of file you download. When I downloaded a kit, I got a ZIP file, but when I downloaded an asset, I got a PNG file. Remember Kees asking you what was the file extension? PNG is the file extension. That is what tells Windows how to open the download. In the case of a PNG file, it's a picture, so Windows will open the asset with a program that handles pictures, not ZIP files. With Windows 7, it opens it in the Photo Gallery application. Since you're using Windows 8, it may use something different, but it WILL open it and display it on the screen.
I've successfully done this with both Firefox 26 and Chrome Version 32.0.1700.102 m. There's nothing wrong with either browser. I think you may just be confused by the different file types.