Think of a diesel-electric locomotive: it burns diesel fuel to generate electricity (ac converted to dc) which drives the engine.
In the system described in the article, aluminum is oxidized by air (in effect “burned”) to generate energy electrochemically, which drives the engine.
One critical difference: one can obtain diesel by refining petroleum you find in holes in the ground (essentially), but you’re not going to find any naturally-occurring aluminum metal.
The “fuel” for the electrochemical system has to be refined using, yes, electricity - and due to losses associated with the laws of thermodynamics, you have to put more electricity into the system than that which you ultimately get out.
So essentially this system allows available primary forms of energy (coal, nukes, etc) to be used in a transportation system. Whether it’s economically viable is another question.
That is the description of every battery.