If relativity is correct, then producing more thrust per power than a photon drive without any exhaust can be used (in principal) to to build a perpetual motion machine. Basically this device claims to violate conservation of 4-momentum, so in the correct frame that is violation of conservation of energy.
If it is possible to create thrust against some sort of background (zero point energy, aether etc), that also violates special relativity by providing a unique reference frame (or violates conservation of energy if it doesn't).
Of course special relativity could be wrong - but it has been tested on scales from quarks to galaxies to black holes. This experiment is not unusual - they are at modest electric fields, length scales and frequencies. There is no reason to expect that after all the tests done on relativity it would be violated by using a special shaped box. Its like the idea that you can build a perpetual motion machine from a special shaped linkage and gears.
I may not be a "top" scientist, whatever that is, but I'm a professional physicist, and have discussed this with colleagues and we all agree that this can't be true without a complete re-write of physics as we know it, We also agree that its a very difficult experiment and that there are a lot of ways that they could have gotten the wrong answer from the experiment.