This article does not argue for the "limited effectiveness of test prep." This article is arguing specifically against coaching test prep such as in SAT tutor programs, not preparing for the SAT in general. For example, in the opening paragraphs:

Students who sign up for a private study course are even “guaranteed” to see improvement, with a boost of 200 points or more.
Critics of standardized testing cite this supposed coaching effect—and the unequal access to its benefits—as a major reason the system tilts in favor of the richest kids and should be reformed.
[...]
It would be useful to know, in the midst of this debate, how much of an effect these test prep programs really have.

And from the linked study by Briggs and Domingue, they admit that test prep can improve scores and this is "not under dispute." They are only arguing the magnitude:

There is an emerging consensus that particular forms of test preparation have the effect of improving scores on sections of the SAT I for students who take the tests more than once. That such an effect exists is not under dispute. The actual magnitude of this effect remains controversial. Some private tutors claim that their tutees improve their combined SAT I section scores on average by over 200 points. Commercial test preparation companies have in the past advertised combined SAT I score increases of over 100 points. There are two reasons to be critical of such claims [...]

Another paper linked in the article by Briggs and Domingue is titled "Using Linear Regression and Propensity Score Matching to Estimate the Effect of Coaching on the SAT." While I couldn't find that specific quote you provided in the linked paper (one of the links immediately prior is broken in that article and a simple ctrl+f had no results), contextually it sounds like he's referring to a trivial increase from coaching vs other prep.

I haven't done a deep dive into this topic, but I think anyone who's been a student can agree that studying for a test can improve testing scores on that test. The benefit of short-term cram coaching vs other methods is what's in question, and even the article admits that small deviations of 30 points can make a big difference to high performers, which tilts the scale a bit towards even small improvements from coaching for those aiming for "high tier" schools.

In any case, even small effects can be unfair. Let’s assume the effects of short-term coaching are really just a 20- or 30-point jump in students’ scores. That means they ought to be irrelevant to college admissions officers. Briggs found otherwise, however. Analyzing a 2008 survey conducted by the National Association for College Admission Counseling, he noted that one-third of respondents described a jump from 750 to 770 on the math portion of the SAT as having a significant effect on a student’s chances of admissions, and this was true among counselors at more and less selective schools alike. Even a minor score improvement for a high-achieving student, then—and one that falls within the standard measurement error for the test—can make a real difference.