The LN2 doesn't actually burn. It's more like a steam engine, where the pressure from the vaporizing nitrogen drives pistons or turbines.
The nice thing here is that the LN2 comes straight from the atmosphere and goes straight back into it. Net zero emissions from the car (obviously producing the energy to compress the nitrogen in the first place isn't going to be net zero, but that's basically the same issue as with hydrogen, electricity, or this ammonia system).