An acquaintance whose family was from Turkey, told me that the pieces move the way do based on ideas about Persian warfare. Moving in a rank or file was considered earthly, and moving diagonal was heavenly.
The king and advisor (queen) are combination of earthly and heavenly power. They are both equal in power, but the king can only move one space at a time, because he is burdened with the weight of command.
The pawns must move in an earthly way, but can only capture with the help of god (so the capture is diagonal like the bishop).
Everything else is fuzzy: There was something about why the pawn's first move could be one or two spaces. I can't remember anything about the knights. There was a reason rooks where earthly. There was also a bit about why castling goes the way it does, and why pawns can be promoted.
Does this ring a bell with anyone? It was a cool story, and I'd like to hear the whole thing again.