When you ask people to name the kingdoms, most people get the big ones, animals, plants, bacteria. Some people may even come up with the protists. But there is one more. Here's a hint. Yeast are part of it. So are shitakes. Are you getting it? Well the answer is fungi.Yes, they are in fact referring to the Whittaker "Five Kingdoms" tree of life, which is no longer in use. (I am placing an image here from my Evolution Textbook) where we talk in Chapter 5 about the history of various trees of life that have been used. The figures from our book are available for free at the book site)
Today we talk about the Three Domains (Bacteria, Archaea and Eukaryotes) and within each of those domains, they are many lineages (which are sometimes referred to as kingdoms). But the five kingdom concept is done and gone. The modern tree looks more like the following (which is an adaptation for our book of a tree by Baldauf).
Mind you, the show on Fungi is worth listening to (although they did miss the opportunity to use the tree of life to answer a question that came up on "Are fungi from outer space?" - the answer should have been - "No, fungi are deeply embedded within the tree of life on this planet, so if life came from elsewhere, it was at the beginning of the origin of life").
Unfortunately, I could not call in to the show (as I have done before) to try and comment on these issues (since I was not listening live). So instead, I am giving Science Friday my Second "Twisted Tree of Life" Award for ignoring the new concepts of the tree of life that have been in play since Woese, Fox and others first laid the groundwork for the existence of the Archaea.