Got nothing to do with cavalry. It's almost entirely the geography, and the situations of the initial war. Khuzait has the least access points into their realms, and right after the initial war everyone is engaged in with some other nation, the odds of Khuzaits entering a multi-front war against 2~3 enemies at the same time, are simply the lowest of all the countries.
Sturgia, otoh, has two large access points west and east. The eastern point is very narrow, and pits them against Khuzait cavalry, which, as a predominantly infantry nation, are disadvantaged from the start. On the western front it has a broad access point that borders 2~3 nations at the same time, and when one town closest to the frontlines is lost, they are bottlenecked and isolated, without being able to counter-attack effectively,
All the rest of the nations are in a toss-up and any nation that gets gangbanged will quickly deteriorate.
That's why in the long-run, the most common situation you see is that of (1) Khuzaits becoming super powerful, (2) Sturgia usually eliminated, (3) everyone else in the middle all deteriorate or get one prominent nation.