I think that's the commentator getting mixed up and not understanding the terms. Jackson didn't say that himself. He probably said that the aluminium cell has a greater specific charge density than lithium. Also, what he's saying is that his battery is small and light. To get the same amount of charge from an equivalent lithium battery, the lithium one would have to be indefeasibly heavy. IIRC, his one uses air, like an IC motor.
I think it's great that all these guys are coming up with ideas and developing them. Sooner or later, some clever person might find the solution we need by combining ideas from several of them. It's only a matter of time. The physics says it's possible, since there's 25 giga watt-hours of energy in one gram of aluminium.
The word 'battery' can easily cause confusion in folks.
the Lithium ion batteries we use are secondary batteries, fuel cells are primary batteries.
Hydrogen air fuel cells for example are primary batteries, you fill up your hydrogen tank. The aluminium air batteries are also fuel cells, and we should not talk about charge density when referring to fuel cells but energy density like you would with a litre of petrol because you have to recycle the used oxidised aluminium to make a new aluminium bar and replace the electrolyte before you could 'recharge' your aluminium air fuel cell.
The main effort in making Al-Air usable is still going on. This guy seems to exploit the fact that it is well known that burning aluminium yields a lot more energy than you can get from rechargeable batteries and we have lots of empty beer cans filling up the rubbish dumps so the benefit of turning empty cans into batteries is easily understood. What is not so easily understood is why other clever people have not done it before.
You can, for example, fill an empty aluminium can with sea water or brine, then dip a graphite electrode into the electrolyte and connect a motor between the can and the electrode and impress school children with your magic but you can't make it a commercial product.
