Sure it is. It's captured by its effect on our overall productivity.
A significant share of the growth in U.S. GDP since the 1970s can be attributed to women leaving the home and entering the workforce. It's not that they were doing any less work beforehand, but a woman who sucked at housework but excelled at piloting an aircraft could work more productively, improving overall efficiency of the economy.
GDP didn't grow simply because her work was now measurable in dollars and cents. People lament that to have a similar standard of living today as 60 years ago, a family needs two wage earners. Yes, and part of the reason is because women entering the workforce _depressed_ wages. In other words, as women earned more money men began earning less. (Except it happened slow enough that men's absolute earnings never declined, they just grew more slowly.) Nonetheless, we're all better off when a woman can make better use of her unique skills. Our economy became more efficient overall, so overall GDP went up commensurately.
Many of the criticisms in that article aren't pertinent to a large, diverse economy like the United States. No economist believes that the GDP figures for a natural-resource intensive economy are as meaningful as for the U.S. They can absolutely be meaningful in some contexts, but are obviously less meaningful in others. Kudos to the journalist for admitting his young naivety, but he's assuming that the his elder contemporaries at the time were similarly naive about the limitations of GDP. The better assumption is that economists in the 1990s that had the same amount of experience as he enjoys today were similarly wise to the limitations of GDP.
Analogies about personal GDP don't work very well. GDP is a macroscopic view that is predicated on various behaviors averaging out. If you had an economy of a single person who only did housework, GDP is obviously useless. But so what? That doesn't say much of anything about it's utility for measuring the overall productive capacity of a huge, diverse economy.
Regarding the relevancy of GDP to Japan... that's why we have metrics like per capita GDP and metrics like the Gini coefficient. Japan is shrinking thus their rate of growth in GDP will slow if not shrink. As a population grows you can asymptotically approach a more efficient allocation of labour and resources, but if its not growing or shrinking you lose out on that avenue for improved productivity. If your entire economy is a single, two-person household, someone will invariably have to specialize in doing housework all day while the other works outdoors. If you have an economy of 300 million, you can out-source both mundane housework and mundane outdoor work and everybody gets more work done overall; certainly more so than an economy of two, but also more so than an economy of 200 million.
But population growth isn't the only opportunity to improve productivity. Japan has a high quality of life partly because of low inequality and thus a low Gini coefficient. Higher inequality tends to signal a more inefficient allocation of labor and resources. Which isn't to say that Japan doesn't have room to improve efficiency (sex inequality is still a big thing), but in many respects they're in a better place than the U.S. to begin with.
Like the the case with natural-resource intensive economies, the Gini coefficient tells us something about the accuracy and meaning of GDP, except in a quantified way. (And if you can't quantify something, you can't easily apply that knowledge.) A high Gini coefficient (and high inequality) suggests that we should be more careful about the conclusions we draw from GDP. In particular it suggests that our presumptions about things "averaging out" are more questionable. Inferences about particular details of the economy will be less accurate, and predictions more volatile. So it's not so much the case that GDP is a poorer way to measure quality of life in Japan, it's that because of our higher Gini coefficient it's a poorer way to measure quality of life in the U.S.
OTOH, it also follows that over the period where GDP growth in Japan has slowed relative to U.S. GDP growth, quality of life in the U.S. has probably in many ways improved faster. The effects mitigated, of course, by our inequality. Likewise, we can find all sorts of fault in how accurately GDP reflects particular details about China, but in relative terms if quite obviously reflects (as expected) a rapidly improving quality of life.