> So does that mean future will belong to societies where woman are not empowered? Because only they will produce kids who shall inherit the Earth.

I assume this is a function of the ability to project force from nation states that observe and respect human rights. If might makes right (historically speaking), you should be prepared to exert force (or offer asylum at scale to women from countries where human rights are at risk or not observed).

https://en.wikipedia.org/wiki/Peace_through_strength

Huh what? A nation may not even need to exert force if it's one of the few ones producing babies.

Ability to defend oneself is a given for any nation state, babies or not.

Well, there are two ways to get population - babies and immigration.