The problem I have with it is that it implies quality-of-life is tied to earnings. That's like saying a single mother working two jobs has a better quality of life than a rich socialite. I know plenty of women who are perfectly happy to be homemakers, work part-time during the day, or teach so that they can enjoy family life.
"Gender equality" the way they measure it here seems to be saying that men and women should ideally live the same. Freedom of choice and equal rights is what matters, and I don't feel that this metric even comes close to measuring that.
Money is a good first approximation of freedom and independence however. And while the extremes you used to illustrate might indeed be uncommon, when we talk about statistics in magnitude of national populations they are not going to distort overall picture.
"Gender equality" the way they measure it here seems to be saying that men and women should ideally live the same. Freedom of choice and equal rights is what matters, and I don't feel that this metric even comes close to measuring that.