Momentum is a measure of kinetic energy, and can also be expressed as a mass term.
The second law of motion is that for every action, there is an equal and opposite reaction. The device SHOULD be pushing particles with the same energy that those particles push back against the device with, which should then be colliding with the back of the device, negating the forward push they initially imparted. However, the particles stop existing before they reach the back end of the device, so they never interact again, and thus never confer that countering momentum, resulting in a violation. The energy simply vanishes along with the particles carrying it-- for all intents and purposes.
This may just be an APPARENT violation, however. The measured laser interferometry data suggests that the fabric of spacetime itself is reacting to this energy disequilibrium, and may in fact be where the energy is "Going." "Empty space" is not a null value for energy state, and fluctuates wildly. The added energy on those virtual particles may be, for instance, kicking the local energy state of the local space to the device into a slightly more energetic condition, which then dissipates over distance as increased vacuum fluctuations, which being completely random, are unable to meaningfully negate the initially imparted momentum, allowing the "reactionless" drive to work, while still conserving the energy conservation law. (Just bending it into some gnarly shapes.)
Spacetime with a slightly different energy density would have slightly different vacuum properties, which would affect how other kinds of forces propogate through it, which may explain the interferometer data. (Some interpretations of feild propogation use models of virtual particle interaction to carry the field. "Anomalies" in the virtual particle density of one bit of spacetime right next to another would create anomalies in field propogation between those regions, which is what the laser interferometer is detecting.)
Being able to exert pressure on the prevalence/rate of vacuum fluctuations would be a radical new development.