Frantz, without knowing anything about the transformer it's hard to say what it's doing, what sort of bandwidth it has, etc. I suspect the stray capacitance around the PCB and transformer plus load is enough filtering. This makes it rather cable-sensitive, which may explain the tale of trial and error muralman1 related. It's not too hard to envision a simple third-order filter (effect) just from those elements (PCB and transformer primary capacitance, transformer inductance, transformer output and cable/load capacitance). In fact, by default it is impossible in a real system as described to not have such a filter; the only question is of bandwidth. Sampling (quantization) noise at the output of a DAC can be pretty broadband so such a simple filter may suffice. That justifies their claim of "no output filter", I suppose. I am guessing, of course...
muralman1, ADI does not list a replacement, only a 16-bit version still in production. The "similar components" list has only delta-sigma DACs; I suspect the conventional style DAC is too expensive (most of the cost is in trim and test) to be competitive, and volume from "purists" like Audio Note is simply too small to justify keeping it around as they move on to other process technology. What AN will do is a good question! There may be other good Nyquist (NOS) DACs out there from e.g. TI, National, Maxim, Wolfson, etc. that AN can use; I have not looked.