I don't know much about the history of chess, but the different pieces obviously represent a social hierarchy: king, queen, knight, pawn are similar to the court cards. Moreover, the number of the pieces is inversely proportional to their rank: each of the 8 pawns is less worthy than the 2 knights, bishops and towers which are less worthy than the unique king and queen. The king is so important that the goal of the game is to defeat it. A pawn can be “promoted” to a queen: the concept of promotion implies that a queen is more valuable than a pawn. The ranking is also represented by the size of the pieces. As in tarot, a kind of ranking seems to me implied by the very nature and rules of the games. If you remove ranking from chess, you get something different, maybe checkers.
As in tarot moralizations, also chess moralizations reflected the intrinsic structure of the game. See for instance:
http://roseandchess.lib.uchicago.edu/chess.html
.... hm ....
Old Chess was different. The Queen was weak. The bishop was weaker than today. Sure, the potential of the possible moves of a type of figure gave an idea, what a figure might be compared to. The Queen was weak, so it was called Queen, cause women are weak in fight. The rook was often a chariot, so he was bound to use streets. He could move straight vertical and horizontal lines, as far the board it allowed (cause streets allow great distances). The horse in contrast could follow its own ways, a combination of diagonal and straight move and jumping. It could "run through a forest", but this was naturally slower as ion a street. The bishop, which jumped one space diagonal, could reach a point, which all other wouldn't get. So he was often interpreted as a bow-shooter. The King was very slow, and needed to be protected.
In Courier-chess they had a "Renner", a runner, and this could move like a modern bishop. Cause the Renner was quick.
The pawn was naturally a foot-soldier, slow. He wasn't allowed to go back. So he was often killed, more than the officers. In Chinese chess they have a cannon. This can jump over one other figure. In Mongol Chess they had a body-guard. If a foreign figure with quick movement entered its region, it couldn't move further, it had to stop. In Shogi (Japanese Chess), you can place captured figures (prisoners) as own figures on the board. Many different ideas of "chess".
The basic phantasy was made from the technical fighting technique. Naturally there were ALSO phantasies, which compared chess with the relevant society. A court, Towers to expand the kingdom in distance to the court, Knights for nobility, bishops for the church and pawns for the rest of us.
Anyway, looking through all the different versions, there were just many sorts of chess with different interpretations. The basic is the phantasy and the result is something, which finally is adapted by others, cause its interesting enough to be called a game. Or not ... then you can play alone with yourself.
Let's take a very modern version of chess, actually a sort of chess-orgasm: "Civilization" by Sid Meier, the mother of a lot of strategy games. You have a board and it may be gigantic and each field can have a number of special qualities (in some versions the board is 3-dimensional; I know a version with 4 levels ... Air, Earth, Water, Underground). You have a lot of opponents with different possibilities to "react". You have a lot of possible figures with different fighting possibilities. One game move may involve hundreds of figures, which fight or move or make other special activities.
The strongest figures are rather obviously the city founders (settlers ... actually a sort of King as Adam + Eve) and the building workers (the pawns).
You have random elements. In the original the game is mirroring the development of human civilization, you start with the alphabet or pottery and end by building a huge rocket to escape the game.
Well, a very complex game. One game may take months and longer. A sort of chess, no doubt, but very, very different.
A chess game at the Austrian courts (16th century) had 32 figures for each side.
In some Shogi developments also the board-size and the number of figures exploded. Such games also needed their time, they weren't naturally not done in one day.
These examples show the interest for expansion of the game. But in pre-computer time something like "Civilization" was not possible to imagine.
One can call this also "game moralization". But "game advertising doesn't change the game", it just has the function of "Fame", in other words "blowing the trumpet".