I can't find a schematic so it's all conjecture.
I'm guessing they accomplish it they way a lot of pseudo-channel-switching is done. The cathode resistor on the section of the tube controls the bias of the tube and a smaller resistor is generally more gain given the same plate load resistor. I'm guessing they are changing the bias on the gain stage using the knob to switch cathode resistors. Cathode resistors also have bypass capacitors to increase gain and shape the response, those are usually switched at the same time.
This is how they do the "more drive" or "boost mode" on a lot of amps including hot rod deluxe, they have two sets of cathode resistor/bypass caps switched with relays so it pops less, it's probably something they just decided to put on a knob this time.