As it works on phase change (e.g. think of melting ice) heat is added (or removed) without changing the temperature of the store (which, I guess, might be hotter or colder than where the heat is extracted or used).
Depending on the needs, resistive heating can get hundreds of degrees hot, but the best heat pumps that I know of can only raise the temperature about 60 or 70° f.
So the way I see it, is that this material should be able to quickly store heat with the using the low temperatures that heat pumps provide, and be able to store it with minimal losses until it is needed.
No, it's about temperature difference. My heat pump water tank heats about as quickly as resistive water tanks; but it could never heat to hundreds of degrees.