That is the new paper this article discusses, but it does not exhaust the research. The author has written other work summarizing multiple different ways of measuring that confirm the same conclusion: http://users.nber.org/~jwolfers/research.php.

More than that, "money is positively associated with happiness/life satisfaction" is common sense. Anyone who has ever struggled with money knows that it's incredibly stressful. "Money doesn't make you any happier" is the counter-intuitive research finding that needs ironclad evidence.

It's also important not to confuse either of these claims with "anyone who has money is happy", which is obviously false. It's still true that money can't buy happiness. But lack of money is a major (but not guaranteed) cause of unhappiness.