You break everything into ELO brackets. 1400+, 1200-1400, 1000-1200 etc. In each bracket you look at the win rate of each civ, how much each civ is picked, any particularly lopsided matchups and also game length. And then you can also filter by map type, so maybe Mongols do really well in 1400+ bracket on open maps, but suck at water and closed maps.
You could also compare average score in the brackets, so on average in 1000-1200 bracket what’s the average food income of an English player compared to a French player. Or what’s the average castle time of a Delhi player compared to a Mongol player.
You can make lots of theories like this and then also every replay is saved on their servers, so they could zip through any replays to see exactly what happened in the game if they thought they needed too.
It’s also possible they are tracking apm across the different civs, and what hotkeys people use and how much.