Wasn't this already debunked as a poor replacement for pumped storage hydro electric? The blocks and the things moving them will always have more wear than water and turbines.
I believe the argument against solid block gravity batteries is that you can achieve the same thing with water by using old mines or even just digging a 40story hole. If you have room for the 40 story tower then you have room for a more efficient pumped hydro hole.
It's not really a battery killer at all. It would never fit or be useful in a car, phone or anything portable. It's more of a possible replacement to pumped-storage hydroelectric.