Few things that need clarifying.
The class requires being lawful, but also says it is available for Bards. Bards can't be lawful though.
Is summoning a chess piece supernatural, spell-like or extraordinary?
And this is just a suggestion but maybe set the ability scores to always be the same instead of determined when summoned. Then the differences between the pieces could be that some are strong but others are dextrous.
Regardless, I was wondering if you noticed that these (presumingly mindless) constructs lack Constitution and Intelligence scores and I believe a Cha of 1. This basically turns the elite array from "15, 14, 13, 12, 10, 8" to "15, 14, 13".
If I'm right about the Cha thing, Bishops might become awkward too. I haven't found a rule about it, but I can't find any mindless undead that have a higher Cha. Also, mindless undead also have a Cha of 1 so it seems to be a trend in the mindless creatures.
The wicked queen ability says normal penalties apply, sort of implying normal bonuses don't.