You are right, Mathilde has done quite a lot in this field of activity. The Princess Mathilde Fund focussed on women´s rights and related topics back in 2004 (women and the multicultural society), 2005 (women and economics) and 2006 (women and health). IIRC the first women´s day lunch was hosted in 2007. Mathilde also participates in many events of Markant, a network of enterprising women in Belgium (being a former enterprising woman herself during her days as speech therapist). During economic trips she tries to support the businesswomen in attendance and also gets in touch with local women: e.g in South Africa (alongside with Mrs. Mbeki) she visited a
SAWID(=South African Women in Dialogue) project and delivered a speech. Not sure if she also zoomed in on female topics during her study of psychology, but it would fit into her profile.
As for her motivation: As far as I understood she emphasizes the power of women due to her understanding of the underestimated and yet central role of women in society. Women´s rights are not taken for granted, neither is gender equality. Women are still disadvantaged and yet they have a lot to offer and this is what is highlighted by awarding projects with the Princess Mathilde Prize for example. So it´s her small contribution to boost the (self-)esteem of women in our society I guess.