Short version:
Unless they believe the machine breaks some of the fundamental physics laws, the device must emit something. With this definition using a red LED Laser powered by a 1.5V battery in the back of the spacecraft is a "no reaction mass" thruster. The problem is that the momentum / energy ratio has theoretical limitations, and they are getting too much momentum.
Long version (based on a previous comment https://news.ycombinator.com/item?id=7162069):
I’ll try to explain what I had understood trying to find an explanations that don’t break the physics laws.
To move the spaceship you need momentum. You must use some particles to carry the opposite momentum away. It’s not clear, but the main candidates are photons (aka light). (The other possibility is gravitons, but that would be even more amazing)
The photons have no rest mass, but they have energy. So to produce them, you must "spend" some energy. The energy source can be carried in the ship (a nuclear reactor) or absorbed in place (solar panel).
If you are using a nuclear reactor, a small par of the mass of the atoms is transformed into energy and you put that energy in the photons. So the net effect is that some of the mass of the spaceship goes away, and it's no long a "no reaction mass" ship. (The same idea is valid to electric batteries, but the mass difference comes from the chemical bounds and not from the nucleus.)
If you use a solar panel, then when you absorb the photons the spaceship gains a little of mass. Unless you have a mechanism to dissipate the mass the spaceship would get heavier. Luckily, the photons that you are using for propulsion carry a little of mass (and the heat you are dissipating also helps). So this is essentially a solar sail, you get some photons, and send them in a different direction, and the change in the direction of the photons give some momentum to your ship. Perhaps a complex setup (solar panel + led) can be more directional that a simple setup (mirror). Perhaps you can gain a x3 or x6 efficiency. (But someone has to do the calculations, because this might break the second law, unless you get a laser light and also dissipate some heat without a specific direction, and the net result as good as a mirror.)
In the previous comment, throwaway_yy2Di noted that with photons "the ratio a photon's momentum to energy is fixed at 1/c, which is 3.3E-6 N/kW". The problem of photons is that to get some moment you need a proportional amount of energy to create them. Another possibility is to create particle-antiparticle pairs and accelerate them, but this is even more inefficient that using photon and you get less than 3.3E-6 N/kW.
The alternative solution is to accelerate other particles (for example the hydrogen atoms in the rocket fuel), you don't need energy to create them, because they are already there. So you can get more than 1/c=3.3E-6 N/kW, but it's not a "no reaction mass" ship.
They claim 40 microNewton/28W = 1.4E-3 N/kW ~= 400000/c. This is in the like 400000 times the theoretical limit, so they have a measurement problem (or they'll get a Nobel price).