It is pumped hydro, but you don't have the same mass of water because of the dramatically different pressures involved. Smaller water mass is the advantage to this, but the problem of managing heat is the downside that pumped storage doesn't face.

This general technique is known as "liquid piston".

Thanks for the search term. I am not a huge fan of the "advanced polymer" wank of that video but liquid piston seems very practical compared most of the "air powered car" nonsense compressed air systems that show up.

I imagine it will get better performance from high pressure water instead of the few psi of a small elevation change.