IQ is held in high esteem because research around g is very good and comprehensive, perhaps the crown jewel of psychology. Additionally most people's knowledge of the Flynn effect is out of date -- recent studies (here's one: http://www.sciencedirect.com/science/article/pii/S0160289615... in fact here's a boatload of references http://www.iapsych.com/iqmr/fe/MasterFlynnEffectreferencelis...) show a rise, leveling off, and then an overall fall from the beginning in performance over the last 40 years rather than the continuous rise (or at least non-decreasing) behavior most people would probably bet on from their layman understanding of the effect. (Additionally ethnic gaps have remained despite controls for everything and it is this unfortunate reality that I think is the reason for so much dismissal of IQ...)
When fairly minor monetary incentives (over $10) can lead to a 20 point increase in scores[1], I'd be wary of reading too much into the tests. As for the Flynn effect, I've read a number of different theories, but there doesn't seem to be any consensus. Given the other issues IQ tests have (like the one just mentioned), I'd be wary about assuming that it doesn't stem from underlying problems with the test itself. Some researchers seem to think it stems from familiarity with test taking in general, which seems to match the general understanding that you will do better on IQ tests if you repeatedly take them, referred to as the "practice effect" (IE, IQ tests at least in part measure familiarity with the test).
This study isn't surprising, I'm unsure what you think it implies. Indeed IQ researchers have been wary themselves and known about motivational effects for decades, along with many other objections to testing like cultural bias and the like that in good modern research are all accounted for -- obviously if I sleep during a test I'll score very low, but if I'm actually awake and care I can increase my score by a huge factor. IQ isn't a perfect correlate, but it's common to reason as if it alone has a predictive power of 0.4-0.6 for various important things, that is stronger than any other single factor we know about. When you add in Conscientiousness (the big five traits being the other contender for psychology's crown jewel, I think), which is about grit, intrinsic motivation, and the like, together with IQ (two factors now, not just one), you get predictive powers of 0.7 to educational success. I would wager that the differences seen in the paper cited by your article are almost entirely accounted for by Conscientiousness, but from the abstract (don't have the full paper) it looks like that was not controlled for at all.
