He said: Is it being loud enough the only concern? What about "dynamic range"?
Given the context of his asking and that he used quotation marks for "dynamic range" I think he wants to know how capable this amp will be for proper driving his phone, how quick it will be to proper accelerate and attenuate the membrane. He is not asking about loud or not, that is already clear to him, I understand. But I might be wrong, as I said.
It depends on what you consider dynamic range.
There is something like DR from DR rating and then there is a dynamic range.
This is is the maximum voltage range / smallest signal that does not drown in noise.
There is also a 3rd 'dynamic range' and is the one you are alluding to.
That is the time it takes for a signal to go from max voltage to a very small value.
It is common belief in audio circles that some amps are 'more dynamic' than others and that dynamics are 'removed' somehow.
This can easily be shown when a needle pulse is measured (an actual one, not the one used to test DACs) where the voltage scale is replaced by a dB scale and the time scale is very short.
You don't see those measurements because they are pointless.
They are sort-of included in square-wave tests.
The 'effect' you are alluding to does not seem to be related to electrical properties but rather is a mindset.
Besides, I have tested such actual pulses on many headphones ranging from the slowest to the fastest around and the limiting factor by magnitudes is the headphone driver, not the amp.
So the question you asked about dynamic range can not be anything other than the second one I described = max SPL divided by the smallest signal you can get from it which in this case is determined by output voltage and efficiency as well as noise floor.
The 70-80dB actual dynamic range is another thing that didn't come out of my thumb either. This is the dynamic range the hearing has when listening to music. As the 120dB is magnitudes larger than the 80dB we humans can actually detect in music the dynamic range is enough.
Then there is a 4th dynamic range which is related to the 2nd and is when an amp does not have enough power and starts to 'soft clip' and fractionally higher levels 'hard clip'.
How hard the clipping occurs and how a headphone reacts depends on several factors. In any case when short clips occur the first mentioned dynamic range becomes smaller as peaks only are smaller in amplitude.
At the onset of clipping and short peaks clipping this does not sound the same as hard clipping from a DAC but more like loudness wars compression. It is not perceived as clipping first but rather as 'pinched off sound'.
This too is no problem in this case as the output power is not that of a phone but much much higher.
When clipping occurs your ears will already have dialed down the volume as it would be too loud.
The stopping and accelerating is not a problem as a: the output impedance is low and b: the amp delivers an output voltage not a start/stop/accelerate/brake signal. It supplies a voltage and the load draws a current.
That output voltage (and the current that belongs with it) are tied together. There is no other parameter.
The driver cannot do anything else then follow the voltage. There is no overshoot or undershoot that is determined by anything else than the driver reaction itself to a voltage change.
The amp in question can deliver enough voltage and current to handle 120dB so this 'starting and stopping' myth is a headphone thing and not an amplifier thing. With high output R and drivers that depend on electrical damping there could be an issue here.
In this case too that isn't a problem.. enough voltage, current and low output R.
I hope this explains your confusion about technical dynamic range and the dynamic range you think exists based on subjective findings and internet myths. It is electronics, mechanics and acoustics (and perception). There is no magic involved nor 'unknown' signals.