I pointed some of Kiltias's points years ago.
The Virgilia vs. Beatrice fight is similar to the game of
Maharajah, with Virgilia as the Maharajah.
Eva -> Evatrice is clearly a pawn promoting.
The Siestas are also compared to bishops in Episode 4, with the comment about the Siestas and a mention of how bishops only attack one color.
When Battler meets Beatrice at the end of Episode 4, he compares himself to the white king, and states that there's still one white square on the board: under his feet. It's impossible for the white king to play an entire game on white squares; he starts on a black square.