The paper claims to settle the correlation-causality question by using a multilevel random effects model metastudy methodology. That seems reasonable to me. However, it completely fails to address the - imho far more important - endogeneity problem, aka: which direction does the causality run (or does it run both ways)?

These results seem completely consistent with a very different story, namely that people who already score higher on those cognitive metrics are more attracted to reading fiction.