People (and even Google) are taking the wrong lesson from this.
The sample used in this study was managers *at Google*. This is a biased sample, in that almost all of them will have high technical competence. So the statistical power of the study in determining how technical competence affects management performance will be low. In some other setting, where managers have much wider variability in technical competence, that factor would very likely show up much higher on the list.
(Analogy: if you conducted a study of how wealth affects cancer survival rates and only admitted millionaires to the study, you might get a very different result than if you also included people with very little money. The classic example of this effect in the statistics literature is a study of wages as a function of height, whose result changes if the sample includes only circus midgets.)