It doesn't appear to have anything to do with the amp, high impedance or not. What's wrong with this picture?
If you think of the amp output impedance and the speaker load as a very simplistic set of resistors in series then you will see that the output impedance has a big influence on the power ultimately reaching the speaker.
Imagine if you were to increase the output impedance to infinity, then the voltage across the resistor representing the speaker would be close to zero - so almost no power reaches the speaker. Conversely, if you assume the output impedance of the amplifier is Zero, then the voltage across the resistor representing the speaker will be a maximum and it will see maximum power.
In practice, there is no such thing as infinity or zero - typically a rule of thumb is 1 to 10 => if the amp output impedance is a tenth of that of the speaker minimum resistive load then to a first order approximation amp ouput impedance can be ignored and the speaker sees all the intended drive voltage (based on the source signal and your volume setting).
What gives tubes the "punch and body" at lower volumes ?
If you understand the above and you think about a typical woofer with a resonance peak at the low end of the bass response (where the impedance may rise from 4 Ohms to 20 Ohms) then it is obvious why a high output impedance amplifier such as one with an 8 ohm output transformer) will sound punchy in the bass, as more voltage/power will reach the woofer at the resonance frequency than in the lower impedance midrange. So in a relative sense the high impedance points get more juice...