Article author here: I do mention the idea of using a chess engine to improve compression. I propose a simple scheme and calculate/estimate my scheme would compress moves in a reasonably played game to about 3.9 bits each on average. I am sure it's possible to do better, but I suspect you'd hit diminishing returns before you get close to 3 bits.

I really should have included something about adding an opening book as I thought about that quite a lot. My conclusion was that an opening book is not going to be a really dramatic win. A simple scheme might encode say 64K opening sequences using 2 bytes, and save an average of perhaps 10 (half) moves. So a saving of 10*4 - 16 = 24 bits, spread over an average of 80 (half) moves. So about 0.3 bits per move.

You might question my estimate of 10 half moves max, but it's an educated guess. One thing I've discovered whilst working on my chess database is that the standard tabiya positions are reached by huge numbers of different transposition possibilities. See my blog post at

https://triplehappy.wordpress.com/2013/11/13/statistics-and-...

This means that the standard canonical way of reaching a well known position doesn't serve as a good proxy for the start of all the games that include that position.