In short, Baron-Cohen has concluded that men are generally better at systemizing, and women are better at empathizing.
Ya don't say....
When my first two boys were born heaps of people gave us teddy bears and soft toys for them. The boys never touched them until they were two years old. Then the toys were made to do a job. They were driving tractors, or going into space, or shooting at possums, or Jesus building a house in heaven!
When Ruth was born I expected the same thing. I was very wrong. From when she learned how to walk she would walk around carrying soft toys and hugging them. As she got a little older she started rocking them off to sleep, shhhing them, feeding them (breast, bottle, and solids), and putting them into bed. It became so common that I found toys everywhere in 'bed', normally with clothes on top of them from out of her drawers as blankets.
She had the same toys, same parenting. The only thing I have ever told her to do differently from the boys was that if she wanted to be upside down (which she is a good chunk of the day), then she needed to either wear trousers or tights so she wasn't flashing everyone, lol.
It's instinctual for girls to be different from boys, that's how they're made. Like the study in the article talked about babies looking at mobiles and faces, they have unique characteristics.
Where I think one of the problems in society lies, is that we then take things that women are good at, like empathising, and turn it into something bad, saying we're too emotional and we cry too much. Then people want to change. Then women think they need to step up and be like a man or they will never get anywhere in life. Instead we should be accepting of how we're all different.