I'm not liking their maths.
For a large shaft, we move weights up to 40 metric tonnes, which give us the capability to store up to 10 kWh of energy per 100 metres of depth.
40t ~= 400kN, so at 100m that's 40MJ. Sure, that's 11.1kWh mechanical, perhaps a little optimistic to say you'll get 10kWh back. That's a smallish home battery.
Where do you get another five-and-a-bit orders of magnitude from, to get to two gigawatt-hours?
Pumped hydro works because water is really really cheap and pretty easy to store, so millions of tonnes of water is doable, whether the height is tens or hundreds of meters.
Steel/iron/concrete is just too expensive. And you can't fit much in a five meter shaft compared to a lake.