I understand that people can and do hunt without a rangefinder. I don't think it's good advice for someone who says they're new to Western hunting. It's not the best way for anyone.
You're right that few people had them 20 years ago. And many people would "hold at the top of his back" or "hold at the top of his antlers" without a real clue what the distance was. Thank goodness we now have accessible/affordable rangefinders and scopes that dial.
Archery and muzzleloader seasons were wounding seasons in those days too. Yes, some guys practiced judging distance and were good at it, but most were not.