Then you're argument is against something that doesn't exist in the articles or study, because the articles and study don't define happiness as being selfish and don't say that it always correlates to selfish behavior.
This is how the article described the questions for happiness:
Happiness was defined, as in the earlier study, by feeling good. The researchers measured happiness by asking subjects questions like How often did you feel happy? How often did you feel interested in life? and How often did you feel satisfied? The more strongly people endorsed these measures of hedonic well-being, or pleasure, the higher they scored on happiness.
There's no moral judgment there, and nothing inherently selfish. Many people in the study that contribute to others, report meaning for themselves, and also report happiness.
The only thing that's correlated with selfish behavior is people that were found report happiness but no meaning. Their reported actions were generally about the self.
The giver/taker part was only linked to the happiness/meaning dichotomy because those are the results of the study. People that reported a lot of meaning tended to be givers. Some people reported happiness and meaning tended to be givers- happiness and meaning were moderately positively correlated. But, people that reported happiness but little meaning, were found to have activities that center on the self. I know people like that in real life, it's easy to think of examples.
They largely let people define their own meaning, but questions were like How often did you feel that your life has a sense of direction or meaning to it?, How often did you feel that you had something to contribute to society? and How often did you feel that you belonged to a community/social group?
