If you want to play against MENACE you can do so here: http://www.mscroggs.co.uk/menace/.
The explanation of how it worked, from what I recall, was very brief, and I didn't understand it much at all.
But it was my first introduction to the concept - outside of my experiences with "science fiction" of the time - that an inanimate "machine" could actually learn. This really ignited my passion for computing and robotics, something I have carried with me since.
It ultimately led me to becoming a software engineer, and to exploring machine learning and artificial intelligence over the years as well.
They aren't. You made this assertion:
... if someone can't comprehend a
paper diagram they can't comprehend
You take the state of the board, find the corresponding matchbox, draw one bead at random out of the box, and make the move.
Depending on if the game is a win, loss, or draw, you add or remove beads in the matchboxes to increase or decrease the odds of making that move again.
After about 150 games or so, the matchboxes almost always draw against a competent opponent.
There is a 1/10 chance that the matchboxes get into a bad state where they can get an empty matchbox. This does not happen in the video.
 In this scenario, the matchboxes always go first. Letting it go second slightly more than doubles the number of matchboxes.