The coke is the fuel that fires the furnaces.
BF is very simplistically a giant counter current reactor. Ore and Coke (the reactants) are added at the top at room temperature and hot gas (the "blast") is injected at the bottom and they flow past each other.
CO is not the only reductant that plays a role Hydrogen primarily from the humidity contained within injected gas also plays a role in the heat balance of the furnace.
Hydrogen is actually very efficient at reducing iron and avoids the CO2 byproduct. I know in the past some alternative ironmaking methods have looked into using things like hydrogen gas and natural gas (CH4) to directly reduce iron ore using a process abbreviated as DRI (Direct Reduced Iron) and for a while in the '90's this was marketed as a Blast Furnace alternative I haven't really kept up with technology.
I started my career as a Metallurgist (Materials Engineer) working at a Blast Furnace they are hugely complicated beasts.
Blast furnaces need fuel to raise the temperature of the blast furnace input to speed up stripping what becomes slag and the oxygen from the iron oxide in the iron ore. Carbon monoxide is what is able to penetrate the iron ore at the high temperatures.
My previous comment is criticizing the author for suggesting that yet another fuel produces the heat for the blast furnace.
Look at your iron-carbon phase diagram: https://www.tf.uni-kiel.de/matwis/amat/iss/kap_9/illustr/fe_...
Cast iron contains a high concentration of carbon, which makes it brittle. To make steel you need a heavy oxidizer to extract the (reduced) carbon. This is usually done using a "basic oxygen furnace", which is basically injecting a high pressure, very high velocity stream of oxygen into the metal to game thermodynamics into combusting the carbon without combusting the iron.
The phase diagram is very interesting too. Very little carbon is needed to go from elemental iron to steel, looks like about 0.008%. Thanks for posting that!
The way I understand it, is that when mined they get iron-oxide, Fe(2)O(3), or Fe(3)O(4), so there is no carbon present.
They use the coke to make carbon monoxide (CO). And this process removes the oxide and adds carbon to iron to create pig iron.
From there it will be further processed to create different steels, alloys and iron products.
Wikipedia (https://en.wikipedia.org/wiki/Iron_ore) under the smelting paragraph describes the oxide removal process.