I don't agree with this line of thinking at all. At the very least, I have found technical expertise to be useful in managers. It helps them draw sane timelines and recognize hard work. At its best, an engineering manager with technical skill is able to guide development away from technical pitfalls, and avoid costly engineering design decisions in large systems. I remember a technical review where a senior Google exec was asked why we needed a specific infrastructure. His answer was shockingly clear: we need x millisecond latency response time from this region, and without this infrastructure, the best we can achieve is x + 200 millisecond. Technical expertise allowed the exec to understand the various issues involved and formulate a clear working strategy.
I have worked with two excellent managers, both of whom are exceptional engineers in their own right, and this has made a large impact in our immediate relationship. They understand the core of my work, they help guide the project towards success, and offer valuable advice when we encounter tricky technical areas. My daily interactions with managers is often on a fairly technical level, because they understand the technical issues. These conversations would be difficult if they had a higher-level view, but not an understanding of the technical core. In a recent project, my manager used his technical insight to plan the project to perfection. The project involved many large changes in infrastructure, and this manager untangled the intricate dependencies to allow everyone to work in parallel. Without his technical insight, this task was nearly impossible.
I suspect the Google study has arrived at a flawed conclusion from the study. All managers at Google are technically gifted, due to the strict selection criterion. Among this selected set, other qualities begin to matter. People skills and clear product strategy are important, but only after the manager is technically capable.
One way to think about it is to look at soccer players. Among all soccer players, determination and team-work are core qualities that predict success. So you could mistakenly conclude that physical strength and stamina don't matter. The truth is that all soccer players are in top physical shape. After they have excellent physical shape, other things start to matter: like their determination, or their team-work.