collegestudent22, I suggest you read Delusions of Gender: How Our Minds, Society, and Neurosexism Create Difference by Cordelia Fine, published in 2010. It addresses your arguments very well and very directly.
The experiment from the lab of Simon Baron-Cohen that HungryHobo describes is only one study, with a fairly small sample size, and not everyone is at all convinced that the experiment was properly blind. The experimenter (one person), who shook the mobile or showed their face, was probably not sufficiently blind to the gender of the baby. They did this in the babies' room, with all of the normal gender cues that very possibly influenced the experimenter's shaking of the mobile and smiling. Also, the babies were shown these things in turn instead of at the very same time, which has an effect on how interested a baby is in something. For this experiment to be the basis of any large, important assumptions about gender, it needs to be done a bunch more times, with slight methodological differences, larger sample sizes, and better blinding. It is possible that infants have different attention preferences depending on gender (but, if I remember correctly, toddler's appear not to, so that's more than a bit weird), but this experiment isn't enough to convince me of that.
I don't know about the specific studies that collegestudent22 linked, but these sorts of studies were also summarized and discussed in Delusions of Gender. How do we know what type of toys are "boy" toys and what types are "girl" toys? How are cars and guns "boy" toys? Clearly, cars and guns, being technological inventions, are social constructions. The idea, existence, and category are social. The things that toy cars do -- wheels roll nicely on the ground as you push with you hand, roll down a slope -- are not the things that adults do with real cars -- drive them from inside, fiddle with the mechanics, revel in the industrial design beauty of the exterior (okay, you can this last with toys, do, but does anyone think this is why cars are boy toys?) are not the same things kids get out of toys. As your link says, previous studies haven't found consistent differences in gender play. Why did this one find differences? How big were the differences? I'd need to read the actual experiment (and a bunch of the other studies) to know if it is convincing or not, and I'm not going to do that right now.
The chimp study is interesting, especially how this stick-play is entirely cultural. The (human socially acculturated) scientists said they'd thought that the girls were carrying the sticks more often, and look, they found that they were right! What's the sample size? Are their gender differences in play in any other chimp groups? How is stick carrying related to moving vs. facial attention in infants? In other words, what's the biological basis across this studies, and is it consistent? At what age do chimp adolescents start to undergo puberty? At what age were these chimps doing stick carrying?
I'm not actually interested in discussing these questions in this thread (or, probably, on this board), because this is the detail and the nitty gritty where I figure out if I'm convinced about science articles. Often, I am not, and, often future research shows where the flaw was in an older study and, especially, the interpretation of that study.
Delusions of Gender has a great section about computer science professionals and the culture of being a nerd. Who is expected to do CS? Nerds. What gender are nerds? Male. In the united states, there is this large cultural expectation that CS is a personality instead of a career, that CS folks are expected to be obsessed with CS and not have many other interests (expect a few other specifically nerdy things), and are expected to spend enormous amounts of time on their job. In other cultures, where even the male CS professionals treat it as a career instead of a cultural identity and obsession, men and women have much much more equal presence in the field.
Engineering preferences might very well be working the same way. Girls are socially expected to be well rounded, to think about a social life in addition to a career or single obsession. Our self-stated preferences are shaped and altered by the society around us (there are lots of good, interesting studies about this), including by whether we check a gender box before we take a career preference test. You can find different gender preferences about getting into the same fields, depending on whether you describe them with words and names for skill sets associated with men or with women (despite the fact that the tasks of the profession are the same no matter which gender associations you put in the description).