If you give the same test to different people under completely different reward conditions, nobody is going to be surprised when the results are different.

IQ tests are far from perfect, but when the same test is administered to different groups under the same conditions it can be reasonable to draw some signal out of the differences between groups.

Generally in a study like this the people administering the test wouldn't even know which group each person belonged to.

It's common knowledge that IQ tests aren't perfect, but your linked paper doesn't debunk their usefulness in a study like this. Not unless the researchers unblinded themselves and offered one group a large reward, which would be a much bigger problem than the use of IQ tests.

You see how that's worse, right? That both intrinsic and extrinsic motivation to comply with the test can swing numbers, so choosing exactly one set of conditions necessarily benefits one group over another rather than creating an environment where everyone performs at their local optimum.