> I expect it is quite more nuanced than his description of dead/not dead and summing up the material on both sides.

It is a bit more nuanced. There are heuristics ( breadth and depth searches ) which assigns positional values and also opening and end game database searches. Using remaining material values is the most basic form of chess engine. If that's all stockfish did, most chess players would beat stockfish.

I built a very simple chess engine for my AI class. I started off with the basic "material values". Then added basic heuristics. Then added database lookups.

Now with neural networks and machine learning, chess engines are even more sophisticated.