I don't understand the advantage of this over just having a digital NN and then pushing the output to some electric motor?
I think you're missing the point. I think it's to demonstrate that fully mechanical systems can learn and react like a real brain plus muscles and sensors. The possible implication is, if consciousness can arise in a digital neural net, it can also arise in a mechanical system, you just need enough of levers and gears connected in a certain way.
That wasn't the point of the research as expressed in the article (note that the final image has a label for "Control electronics" underneath the mechanical system):
> Thus, this work lays the foundation for artificial-intelligent (AI) materials that can learn behaviors and properties.
With applications such as:
> use in aircraft wings to morph the shape in response to wind patterns to boost efficiency, adding reactive rigidity to buildings to better withstand earthquakes and other disasters, shockwave-deflecting reactive armor, or even the creation of surfaces able to perform acoustic imaging.