I didn't read the link but the distinction in the text you quoted seems to be making the same point.
We can "feel happy" and know it just by observing the feeling (which is pleasurable). But if we start looking to evaluate "happiness" and whether we meet that evaluation, it's a much more intellectual process that involves a lot more than feelings.
I actually think "joy" has the same issue (and really, the issue is not with the particular word, but with "words" in and of themselves). I can no doubt feel it when I am joyful, but if I were asked to sit back and construct a written definition of the word "joy," that would be just about as difficult as the word 'happiness."
I think the issue that has to be articulated is that we have to be clear that "feelings" are the true guide of life. We can do out best to construct "maps" and write down all sorts of definitions of "happiness" and "pleasure" and "joy" and eudaimonia and everything else, but in the end we have to be clear about the limits of words. Words are maps and they are highly useful, but elaborate definitions can only serve that "map" function -- they cannot be equated with or confused with the feelings themselves. Trying to equate them in every respect leaves us confused and frustrated and shouldn't even be attempted without first making clear this difference between feelings and concepts.