From the paper it seems like they did build a demonstrator to test their model. This is of course very far from a practical power supply, but you can definitely scratch the could. The only question is how this scales.
But seriously... stuff like this ("ZOMG MIRACLE BATTERY! MIRACLE SOLUTION! ZOMG!) seem to disappear because it takes years to turn an idea into a demo... and longer to get a demo to market and to scale.
We are surrounded by stuff that followed that route but I hope stuff like this actually makes it to market.