The way nature intended?
You think that for the whole of human history all the menoff somewhere else while the woman was screaming her head off?
The human race in modern terms has been around for some 50,000 odd years, recorded history is around 6000 years or so, so for all that time in all cultures the men leave their women to suffer during childbirth?
Rules of what game? Marriage is not a game, bringing kids into the world is not a game, at least not in my book!
I think for myself, I always have, I don't slavishly follow some hypothetical male behavioural handbook the way so many of my brainwashed schoolmates of old did (actually most of my mates were quite independent thinkers so I am being unfair)
If the delivery room is not for you then maybe you have a weak stomach or something, you are certainly free to have made your own choice and that has to be respected but you are just one guy and the rule book you are quoting from is not one that I respect and it would appear that neither do a lot of other guys on here.
I seriously think that those that adhere to your "rules of the game" are in the minority these days, however it is often easier to go with the flow than to think for yourself, in my view people with "backbone" are the ones that can go against the flow and make their own choices in life!
Jim