Indeed, moral dimensions in board games go back to ancient times. The Egyptian game "Senet", which is over four thousand years old, seems to have religious significance, reenacting the voyage of a soul after death into the afterlife. Since religious rituals commonly replicate a large, sacred concept on a small scale, it makes sense that a board game could get involved.

Doing some light Googling, this seemed to be a good writeup by an academic on the subject: https://piccionep.people.cofc.edu/senet_web.html