Whether you put the choke on the input or the output the effect is the same. A transformer reflects the impedance from one side to the other based on the turns ratio. Even if the inductor is on the front AC side, it still effectively forms an LC with the capacitor. Note Schiit's Description. It works, but is it is a good engineering idea? Questionable. The "custom nickel core" sounds all impressive, but that is just common core material and custom inductor is not remotely difficult.
And pure LC—inductor-capacitor filtering from the highest to the lowest band, including 4 custom 80% nickel-core inductors as big as 1.5 Henries.