As a parent, you are supposed to make the choices that increase the chances of better outcomes for the children, whatever the parent considers those better outcomes to be.
This kind of thing was huge in the Chinese community when I was growing up. Every child played chess, was taking violin or piano lessons, was a member of the debate club, was vying for a place on the student council, was in AP classes, was being driven to so many extracurricular activities (chosen by their parents of course), and was downright MISERABLE. One even committed suicide.
Meanwhile the rest of us would go out to wherever we wanted (by bike usually), do whatever we wanted, came home by dinner, and had a wonderful childhood.
Introduce them to many games, sure, but then back off. Once you start directing their play or supervising their play, you do more harm than good.