He stresses regularly spaced sampling. I don't see why high-precision timestamps wouldn't work just as well, though that would complicate the computation of the I and D signals.

Actually, throughout he doesn't seem to acknowledge the different units between the P, the I, and the D, instead implicitly treating the whole system as discrete time for many purposes, in e.g. the recommendations for 100:1 ratios between P, and I; and D and P.