1) Trends are not absolutes and should not be applied to every individual.
2) One small study is not comprehensive.
3) Gendered treatment starts from birth and in some cases even before birth, so the initial predicate of that study is false and thus its conclusion is unreliable.
4) Other studies have shown no distinction.
The study you refer to was not double-blind. Not by a long chalk. It was directly administered by one of the authors of the study who had decided beforehand what the results were going to be and who had constant knowledge of the factors involved. Even if she was trying not to bias the results, she would have been biasing the results. That's exactly why studies are usually constructed to make everyone involved on both sides ignorant of the factors involved.
Then there's the mobile used. It was made from an image of a face with bits moved around. Same individual parts of the face, arranged in different positions and with different lighting in some areas. Were the babies who spent more time looking at it doing so because it was not a face or because they were shuffling the image around in their minds to try to reconstruct the face? The authors of the study assume the former because it helps their preconceived ideas about innate female superiority, but that doesn't mean it was really the case.
Then there's what was actually being measured - chunks of time as short as 3 seconds in which some people judged where the baby was looking. A tendency to look at the face more than the mobile was assumed to be a preference for looking at faces, which was assumed to be superior socialisation skills. Was that the reason or was it taking them a bit longer to recognise a face?
The authors of the study assume the former because it helps their preconceived ideas about innate female superiority, but that doesn't mean it was really the case.
So people who assumed things about gender made a study to create evidence for their assumptions and made assumptions about the interpretation of the evidence to support their assumptions.
Our society is so fixated on sex and genderisation is so deeply engrained that it is normal to not even be able to think about a person without knowing their sex because even thinking about someone is gendered. The most common first question about a neonate is their sex - "what did she have?". That question contains the assumption that a person's sex is their identity, that their sex is
literally what they are. Then genderisation can be imposed on them as if it was sex, which is why it's normal to require knowing a person's sex as the first thing about them. That's why it's normal for people to treat people differently depending on what they think the other person's sex is, right from birth. This has been shown repeatedly by giving adults false information about a child's sex and observing their interactions with the child. In some cases, the
same child dressed differently. Put an infant in blue clothing, tell the adult the infant is a boy. Later on, put the same infant in pink clothing and tell the same adult that the infant is a girl. That's all it takes.