As negiarcian says, I assume those publications are using the MOBI periodical format. There's no documentation that I'm aware of on that format, and no way that I know of to create it directly, though it might be possible to create a "recipe" to create it using Calibre - see the following thread:
https://www.mobileread.com/forums/sho...d.php?t=110646
In an ordinary MOBI book, the only functions of the Kindle 5-way controller that I'm aware of being able to influence in any way are when it is rocked left or right while reading a book - if the MOBI file contains an NCX file defining navigation points in the book (such as the start of each chapter, for example), then rocking the 5-way controller left or right will jump to the previous or next navigation point.