As much more of an expert on signal transformers than most, I'd like to weigh in here.
What the measurements & audible results show is not *endemic* to using a transformer. Rather, it is primarily a result of using a VERY poorly selected and/or shockingly bad transformer, as far as specs and/or quality. It is clear to me from the graphs that there is a very bad mismatch between the transformer chosen and the capabilities of the circuit driving it. Even if it were a Jensen transformer(which I consider *second* best current maker, behind Cinemag), if it had same or similar specs to whatever cheaper unit was used, the results would be similarly shockingly bad. Problems can be further exacerbated by mismatch on secondary side. So, if, say, the secondary Z is 600ohms, it would be quite meaningful to run tests with various loads(assuming I am correctly reading that the transformer is the final output of the dac), from 600ohms to several steps up to 10 or 15kohms. But I do think this would simply confirm that the main issue is a drastic mismatch between driving circuitry & transformer primary.
The reviewer gives a perhaps unintended impression that transformers are always bad in a signal path. IMO, this is very, very untrue. When done properly, using a transformer is quite often the superior way to go, e.g., for balanced input of preamp/amp, it's rather hard to design a transformerless differential input that doesn't color the sound more than a well-selected transformer. Opinions may vary wildly, but, in my >40 years of pro experience, this has been well demonstrated in practice.