The video at the bottom of the article is the inventor detailing the math behind his work. While math and I don't get along very well, his explanation for why the drive doesn't actually violate known physics appears to hang together. It seems like he's saying that what happens inside the resonance cavity follows the rules of relativity, with net thrust being applied to the inner surface of the larger end of the resonance cavity. Since one end is thus being pushed harder than the other end, the result is Newtonian motion of the structure in the opposite direction.

OBTRAV: Assuming I'm interpreting the drawings in the second video correctly, what we see poking out of the back of Classic Traveller spaceships is the narrow end of the resonance cavity . . . which is glowing due to waste heat.