Executive Summary: Solar heater that can work at temperatures close to 1000C by using semi-opaque materials to absorb solar energy and minimise radiative losses. Not even a proof of concept of an improved smelter.
Article text in PopMech is exaggeration of paper and headline is a further exaggeration on top of that.
Solar process heat at above 1,000°C can decarbonize key industrial applications such as cement manufacturing and metallurgical extraction.
The article is just running with that theme.
... so what's the reducing agent, if not carbon?
There are multiple roles for heat. Most notably, most of the necessary chemical reactions require high heat to occur at a time. Furthermore, outright melting gives the advantage that impurities tend to sort themselves by density, and your impurities are typically less dense than your main metal (i.e., the slag will float on top of the molten iron). There's also the advantage that high heat can make volatile impurities (e.g., sulfur dioxide) boil out.
Historically, the reducing agent was largely charcoal, where you burn the wood in oxygen-poor environment to produce high purity carbon-rich material. The industrial revolution replaced charcoal with coke, where you burn coal in oxygen-poor environment to produce high purity carbon-rich material. In both cases, the furnace converts the fuel largely into carbon monoxide, which is the main actual reducing agent in contact with the iron (whereupon it forms carbon dioxide). The decarbonization assumption has been to replace carbon with hydrogen gas, but as far as I'm aware, hydrogen-based reduction furnaces have only existed in pilot plant form.