The files are rendered within a table showing Filename, Size (MB), Date (of modification) as well as the 'download counter' showing how often each file was downloaded.
I wonder how to realize that feature in Tiki? The first thing which comes to my mind is to use the data recorded in the File Gallery, but wonder if it can be available in front-end or it is usable only in the back-end?
Tiki doesn't really have a front-end or back-end, it's up to you who you let see what, so you could give access to anonymous for file galleries (or just that one) and set up the fields displayed to suit - and if people can't upload or edit stuff then those buttons and options just don't show for them. It's the WYSIWYCA principle!
Alternatively, if you want more control over the presentation and want to do it in a wiki page you can use the unified search index of course, and display what you want using the list (or custom search) plugins. There's a similar example here: Carousel_Formatting