You can do a lot of things with electricity: you can heat things, but also move them around and run your TV, all without any loss. With heat you can just... heat things. So you can't call this an "iron battery", because you don't get electricity out of it, just heat. Maybe call it a "heat battery" or "high performance heat pad".
Also note the efficiency numbers: "High-efficiency electrolysis of iron oxide can store as much as 80 percent of your input energy in the iron fuel" is the efficiency of the process itself. "Using this kind of cyclical process to generate electricity could approach a theoretical efficiency around 40 percent" is because you need to climb the ladder to low entropy again (probably by using the equivalent of a steam engine to run a generator).