Keep in mind that $75,000 isn’t supposed to be a hard number. It’s an average based on the data they collected, and it would of course vary based on cost of living. The other important thing to keep in mind is that there is not just one concept of happiness. The Princeton study you are talking about was specifically concerned with life satisfaction (the feeling that one’s life is going well). This is a sort of “overall” happiness, as opposed to the emotional ups and downs of daily life.
All that said, we have built a society in which one cannot easily go without money. You need a certain amount just to survive, and an even higher amount to be secure in your lifestyle. It is not surprising, therefore, that people with less money than they need to survive are extremely unhappy and that people with less money than they need to be secure suffer from a constant, even if low-level, amount of stress. It is also unsurprising that once someone has enough money to be generally secure and not have to worry about emergencies, they tend to be more or less satisfied with their life (with extra money creating variations only in other types of happiness).
But there is more to it than just money. There is also attitude. “Enough is abundance to the wise,” as Euripides said. While the society we live in requires money for security and survival, and while there are hard limits on how little we can make before we start losing out in these areas, our notions of what counts as “enough” also contribute to our perception of how close to these hard limits we are. If I exaggerated beliefs about what I need to survive, then I will feel stressed sooner than someone who has more accurate beliefs in this regard. The same is true if I have exaggerated beliefs about what I need to be secure. For someone with wildly incorrect beliefs in this area, $75,000 might not be enough to calm their minds.
Luckily, we can—within limits—modify our notions of what counts as “enough.” And in fact, there is a lot of related research that tells us how we can most effectively spend our money in the pursuit of happiness. Experiences make us happier than things (sorry industrialists). Giving makes us happier than receiving (sorry egoists). And as the Princeton study shows, reducing worry is one of the best ways to increase life satisfaction. This isn’t the worldview most of us were raised with, but discarding the notions society tries to sell us costs nothing. In fact, it just leaves us with one less thing to buy.