The power of labelling. Imagine there are two identical pairs of socks. Same colour, same size, same shape, same everything. One is labelled "men's" and one is labelled "women's". Is that different labelling of an identical product really enough to make it important which pair a person wears?
It's not so much the labelling but rather the differences in style and size with men's and women's watches in general. It's not like you walk around with a label on your watch saying "men's" or "women's" so the analogy re: labels on otherwise identical socks is a bit moot.
Having said that some women will buy men's watches, actress Helen Mirren does this for example. I think if someone was really into mechanical watches in terms of the technical aspects, complications etc.. then they'd perhaps have more choice among men's watches whereas women's watches tend to be more just jewellery items.
The same watch is also labelled "unisex", by the way. Does that make a difference to how you perceive it? What if I decided to label it "men's"? Would that make a difference to how you perceive it? If labelling is all that matters, does it matter who labels it?
No, not quite, the same watch isn't also labelled unisex but rather a larger version of it (I guess the general design itself is), you get a different watch of the same style if you click on unisex - the case goes from 27mm to 36mm and the width of the band increases too.
for reference, this is what a 26mm watch look like on someone's wrist:
Women's watches tend to be smaller and have thinner straps, you wouldn't need a label to see that the above is a "women's" watch.
Now below are 36mm, 40mm and 44mm watches. Lots of men's watches are 40mm+ these days so you can see why 36mm might be chosen as the size for a more unisex watch: