That thing will work, but it will take a long, long time. Cigarette lighters, or "power points" as they are now called, are typically fused at 5 amps. The internal wiring won't handle more than that.

If you look at the size of the wire on that gadget it's rather small. Compare it to the wire of your typical battery-to-battery jumper cables. Even those cables can get hot if it's a long crank.

The usual "jump start" charger will kick out between 50 and 60 amps, and that may not be enough without charging the battery for a while first. A battery-to-battery cable connection can handle much more current than that.

If the battery is completely deat, lights left on sort of thing, I would anticipate spending 8 or 10 hours charging with those things even before even having a chance to start your car.

That's a long time for any kind of jump.

Arf