First-of-all, I think, like someone else said, that the female posted it, thinking it would make her seem educated / cool / cultured / whatever.
Secondly, I don't have a problem with the quote----but, I don't take it, so literally. I agree that Shakespeare wasn't saying "win a woman's heart", but that he totally meant "win woman"----but, haven't you ever heard the saying: "A man chases a woman, until SHE catches him"? It's the same thing----the "prize" is love (there's your object), LTR, and marriage.
When we read things like that, from back-in-the-day, and apply TODAY'S standard to them, sure, they can be construed, as sexist----but, IMO, if we just look at / read it loosely / generally / whatever (NOT literal), the overall message, is what's important (to ME, anyway): to win love (and that's romantic, to alot of people).
_________________
White female; age 59; diagnosed Aspie.
I use caps for emphasis----I'm NOT angry or shouting. I use caps like others use italics, underline, or bold.
"What we know is a drop; what we don't know, is an ocean." (Sir Isaac Newton)