That bit about games reflecting family roles seems like a stretch. People play board games to relax, not to act out some deep family drama. Your mom might just be competitive at Monopoly but totally chill in real life. Reading life lessons into every game night feels like overthinking it.
Setting ground rules reminded me of my uncle's chess tournaments. He'd spend more time debating move timers than actually playing. It became a whole thing where the rules were the real game.