I don't see similar filtering in the Hoffman design. I wondered if I'd missed it, or perhaps the Hoffman design is a constant-current design, which IIUC does not need such freq-response treatment.
Constant current is what you always strive for (at least for the frequencies of interest) because the current is what makes the magnetic flux that twists the springs and you want all of the frequencies to activate the springs the same.
The input coil on the tank doubles its impedance with each increasing octave. In order to have the same current when the impedance doubles, you would have to double the voltage which is +6dB.
There is more than one way to achieve a voltage that increases at the rate of 6dB/octave. Op Amp drivers typically place the input coil in the NFB loop so that when the coil impedance doubles, the NFB drops in half and the output voltage of the Op Amp doubles.
The 6G15 utilizes a driver transformer that reflects the tank input coil impedance to the primary. The 6V6 puts out about the same current regardless of the plate voltage, so when the impedance of the primary of the driver transformer doubles, the voltage across the primary also doubles. When the primary voltage doubles, the secondary voltage also doubles so that the input coil gets a voltage that increases at the rate of 6dB/octave.