I don't think these devices work in the same way as a conventional car battery judging by the thickness of the cables which connect to the car battery.
My thoughts exactly - those puny cables and the socket they plug into would act like a fuse if you tried to pass any appreciable current through them, especially the 800 amps claimed, even for a very short time. I think they transfer some power to the vehicle battery.
You would be surprised how much cable will conduct without ‘fusing’. In addition car starter motors take a very high inrush current when they move from standstill. Once they start turning the current drops so this is not a continuous load.
One other factor to consider is that the battery is only rated at 20 Ah so could only ever supply 800 A for 1.5 minuted. Yes the cable would get very hot if this scenario ever occurred but it would not ‘fuse’.