It appears to be a fresh combination of existing technologies. You can get off-the-shelf high voltage switching power supplies that are smaller and lighter than conventional power transformers. Output transformer-less (OTL) circuits have been around for decades, as Anacephalic points out. I think that many of the designs are engineering exercises--mental challenges, not necessarily a great leap forward in tone or audio fidelity.
Here's a page on OTL design for the curious:
This guy even sells a board and experimenter's kit so you can build your own OTL amp.
As Johnny Crash says, our ears are trained to the kinds of distortions produced by output transformers, however slight they might be. Audio transformers have been around for 100 years and have gotten rather good. It wouldn't surprise me if the Milbert amp had some voicing in it to tailor the frequency response to players' expectations. Compared to transformers, speakers impose far greater distortions and limitations, so I'm not all that impressed by OTL designs.
The hi-fi megasnob, however, could have a direct-coupled (no capacitors) OTL system driving planar electrostatic speakers for the ultimate in perfection. The technology is wonderful, but insanely expensive.
Today, power transformers, diodes and big electrolytic caps are still less expensive than a 400-500V switching power supply, but who knows, maybe it's time for that technology to trickle down. Ditto for OTL. A 35 lb. Twin Reverb would be pretty cool.