This is probably wrong. We know from the stats that power belong to those who show up. The religious are showing up from a demographic standpoint due to above-replacement-rate fertility. Rationality can’t choose when a child should exist with much confidence; the delay causes the slow degradation of the ‘rations’ institute.
That could spell the difference between sane rational games and crazy rational games right there. That presence or absence of empirical grounding.
And on the flipside, we are all familiar with games that are rigorous, with good logical consistency, but founded on thin air. Dogmatic religion, videogames, fiction...
Our archaeology and history have had trouble grasping this, since the idea that power is its own end is so deeply ingrained in our (western) civilization. But it has not always been the case. David Graeber and David Wengrow's "The Dawn of Everything" illustrates this with evidence.
The reason we value the games of rationality and science over the games of religion and mythology is that the former games produce significantly more power.
And that's the ultimate game of life. Crudely, might makes right. Those individuals or groups that can most effectively harness various forms of power to first defend, and then extend, their claim of limited resources win the game, by simple virtue of the fact that they remain while their competition fades away.
But even games like religion have been, and continue to be valuable frameworks for this ultimate game. There's a strong argument to be made that religion binds large groups of people together towards a common goal and incentivizes individuals to sacrifice the entirety of their life because they believe their rewards will come in the non existent afterlife. That's a powerful game, if you can keep the fantasy alive.