(Slight technical correction: It definitely has a gearbox -- just not one with multiple speeds.)
I think this is the most interesting powertrain concept in a long time. It's definitely one of the VERY few things that has legitimately moved the supercar game on. It's a quantum leap ahead of what Porsche, McLaren, and Ferrari have been doing with their halo cars.
Still awaiting a full technical explanation, but here's what I've gathered. Basically, the combustion engine is permanently in whatever gearing would get the car to 248 MPH at redline. That's obviously way too tall for low speeds, which is why it's connected via a viscous clutch -- it can act as a generator and assist the electic motors, which will do most of the work until the car is going fast enough for the engine to take over. So, you get electric torque at low speeds, and combustion engine power at high speeds.
Plus, the fact that each rear wheel has its own motor means that the car can do some neat things with torque vectoring. If Koenigsegg did their homework, it could be a step ahead of a traditional limited-slip or torque-biasing diff.
Really interested to see how this pans out in practice.