The technique can detect the intersection point of a (fixed size, axially aligned) moving bounding box and a hull defined as a BSP tree. In this sense it is rather limited compared to newer methods but it works rather well and the implementation is pretty robust, and fast enough for the primitive hardware of the day.
Hello, video creator here. This is indeed the actual code, and it is written in QuakeC, a language created specifically for the game logic in Quake. The part I'm not sure about is why the creators wanted to add in extra side beams at all.
I love this write-up, especially the interactive diagrams at the end. My vid doesn't go into as much detail on the actual circuit design, but like the article it uses a bunch of BCD ripple-carry adders. For output I use standard 7-segment decoders. As noted in the comments there are faster ways to do logic in Quake which I overlooked in my research, but to my knowledge noone has made a circuit this large before. I've put the source code on github for anyone that wants to take a deeper look: https://github.com/matthewearl/q1logic/