How does this fit into the wider picture of steelmaking with electric arc furnaces? Those have been around for a good long while; what can this do that an electric arc furnace can't?
Pretty much nothing, at least for steel. You still need the carbon to incorporate into the alloy so like arc furnaces, they can only be used with mostly scrap material. That’s why steel makers still use coal. They need the coke.
IIRC steelmakers use roughly 2 parts iron to 1 part coke, which means coke would be 33% of the weight, but steel is only 1% carbon - that's an efficiency of only 3%. Metallurgical coal is used primarily because it burns hot enough to efficiently melt iron.
> Metallurgical coal is used primarily because it burns hot enough to efficiently melt iron.
That’s the historical reason, but now it's used because carbon is a reducing agent that binds to oxygen, preventing it from oxidizing the iron back into iron oxide and because the coke is used as a permeable membrane to let the resulting gasses escape.
If it was just a matter of heat, there's any number of cleaner fuels steelmakers could use but they can't because the coal serves an important role in the chemistry of blast furnaces.
Electric furnaces introduce carbon using graphite electrodes which is enough for the carbon that gets embedded in the alloy but to convert the iron oxide in raw ore to pure iron in a blast furnace, you need a lot more carbon as a reducing agent to bind to oxygen, preventing it from oxidizing the working material as the metal cools. The coke also serves a dual purpose as a semi-permeable solid that allows the hot gasses to escape from the furnace without collapsing under the weight of the molten metal.