The engine fires for three days to set up a mars transfer orbit. Contrast this with the trans-lunar injection with the S-IVB rocket that was used in the Apollo program, which fires for 350 seconds. Mars is a lot farther away than the moon, but this was the only figure I could find with a quick wikipedia search.

That sounds powerful to me. However, they also talk of pulse rates of 14s to 3m (slide 19). I guess you will have to divide that power output by some duty cycle (corrections welcome; I only browsed the PowerPoint, and wouldn't understand it, anyways)

Biggest weight point is the fuel with 320 tons... I wonder how much fuel is needed for the same energy output as the A380 engines.

I would say it is unsuitable for atmospheric engines because of the way it runs. Earth to Mars in 30 days will need you to be travelling at almost 90 km/second. The engine has to fire for 3 days straight because the delta v you need is retardedly high, so it pulses the engine once a minute so that the passengers don't die and the ship doesn't break up due to huge g-forces.

Lifting something into orbit needs to be done fast, because most of your energy is spent counteracting gravity, not air resistance. A slow pulsing engine would not be enough to get you up.

(Good reading is the specific impulse article on Wikipedia: http://en.wikipedia.org/wiki/Specific_Impulse )

At any given point, our technology allows us to create highly efficient but relatively "weak" engines (e.g. ion thrusters), or "powerful" but inefficient ones (e.g. rockets). Actually, both use Newton's second law to generate thrust, i.e. some kind of material has to exit the engine in the opposite direction, in order to get things moving. So, even ion drives and similar designs carry some material for the purpose of being ejected, it's usually just on a completely different scale to rockets. Energy also needs to come from somewhere to facilitate this, with rockets, it's the chemical energy from the fuel itself. With ion drives, it is usually some form of electricity, generated with a solar panel or nuclear power plant, etc.

So in reality, even the efficient drives also have to carry some way to power themselves. To get more thrust, they need to have more power. If you run the maths, by the time they have enough power to overcome Earth's gravity, they need to have an entire solar farm worth of panels (which are heavy), or a rather large nuclear power station on board (which is also quite heavy). So, unless we find ways to make more powerful sources of energy, or even more ridiculously efficient drives, the thrust coming from these will not be able to overcome near-Earth gravity.