How does one activate the 1 click to skip story? I have the option enabled in the menu.

Lest I forget. I found the answer to this (after beating most Chapters).

There is no default button for this so you must manually assign a button in the menu to activate this.

It seems like a strange oversight but this is part of the reason why I gave the non-casual experience a lower score in my review. Unfortunately I did not have enough room to mention it there as I hit the character limit.