If you step through the lookup table with constant size steps, you would get a sine wave. If the steps are not constant size then you get a distorted sine wave. The "rate of change of the phase angle" would then be the step size.
What is usually called frequency, and has the same value in boring cases like an unvarying sinusoid, is the inverse of the period of the resulting sound as someone would hear it, which is not instantaneous and needs on the order of one period's worth of samples (usually more) to estimate, for a certain definition of period (e.g. interval between zero crossings) or a certain mathematically reasonable calculation (e.g. estimating the frequency of the strongest component from a fixed-length window of past samples).
Everyone is absolutely right that this is the same as frequency. I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram. Quite likely I picked up that exact phrasing of "phase angle" from some academic literature in particular.
That's a lie, because:
> I think I was used that particular poetic flourish to emphasise how complicated the academic, mathematic explanation is, in contrast with the diagram
is a totally different to what the person you are replying to said