While I agree that the system needs fixing, I disagree that we are unhappy because of that fact. I think it's an easy thing to complain about, and that life is a lot easier with money than without. Unhappiness, however, is a bedrock of civilization, and we wouldn't know what to do without it. Bertrand Russell wrote The Conquest of Happiness back in 1930 where he mused about why the current generation thought they were the unhappiest (Modernity! Unemployment! City Life! etc), and then went on to point out that everything he could find in the literature pointed to every generation feeling this way, only the specifics of what made them unhappy changed. This all isn't to say that I don't think we need a radical reorganization of how our basic tax and wage structure operates. On that front I agree (and I'm one of the luck ones; I have some student debt, but I don't struggle to pay my bills). Perhaps in a coming election cycle we'll see the Tea Party finally be the catalyst the social change that they fear so much. That is, maybe the party will implode, and the tax code can be reworked in a way that is more favorable to the younger generation (after all, social issues are mostly bullshit; gays getting married is nice and all, and I'm happy for them, but tax law is all anyone should care about if they want a bigger slice of the pie--those other things are side shows that keep the focus off of real problems). I doubt it, as we shan't be writing the law, but one can dream.
I believe the article is saying that having to work menial jobs to get by while making your employer rich while our financial system is designed to make most people poorer and poorer is what makes us unhappy. You are right though in saying every generation has something to point at that makes them unhappy. Happiness comes from within, but your society can certainly contribute towards your unhappiness and our current society has quite a few absurdities abound.