Actually it does have something to do with voltage gain. Depending on the ratio selected, assuming your source was 2V output, voltage gain could be stepped up to 4, 8, or 16V. Then you would attenuate the signal from there.
The circuit design loads the signal source op-amp letting it operate at its maximum ability. It is a completely passive design (no active circuitry, no power supply, or power cord), but unlike other passive pre-amplifiers, the MLA delivers a higher voltage at its output than it receives from the input. One benefit over other passive designs is the output impedance remains fixed which means that the frequency response does not change as the volume is changed.
The whole concept works due to the nature of how the hand built nickel core transformers are wound and operate. These are essentially op-amp loading transformers that cause op-amps to deliver current into an essentially pure impedance primary. The secondary then produces the equivalent voltage into hard termination which is now usable for the next stage of amplification.
So, like an active preamp it offers its own version of gain, but at much greater transparency and lower distortion levels. It does not use buffers. Call it an in-active preamp if you would. It is best used with digital sources under 600 ohms, but I have a high impedance (10K) input as well for use with tube and other sources requiring it. I also have used it with my phono stage, but it uses AD-797 op-amps for the output so it matches up better than other phono stages might. I'm working on a balanced version that will sit between my Otari Mx-5050 BII and Atma-Sphere S-30.
