Well the article paints a pretty clear hypothesis, if you read it -- dowries are rooted in the idea that in a particular kind of society (not the ones where a household is losing out on a woman's labor and hence needs a bride price), the woman who is married off into her husband's household is seen as a burden, an outsider, one more mouth to feed.

Therefore a dowry is both compensation, and a demonstration of value (i.e. take my daughter because she has a high dowry, and is thus more desirable to marry than other girls with less dowry).