Per square foot. People often refer to watts per square foot, but that will also include all the waste heat generated. Par watts per square foot is a more direct indicator of radiant intensity. As you have noted it doesn't take into account the spectrum or optical considerations, but that doesn't skew the results enough to keep it from being useful.
What does PAR watts mean? Is it even relevant to growing? (just following up to continue the discussion, not being critical)
Plants are photon counters. From research, we know there are 2 systems, PSI and PSII, that use 680 and 700nm photons. The plant has to condition photons of shorter wavelengths to 680 and 700nm in order to use the photons. This is done by reducing the energy of the photon with the energy typically wasted as heat.
PAR watts includes any photons that fall in the PAR range for an amount of power. It doesn't include the SPD so there is no idea of how many photons are created by the light source. They could be mostly blue, meaning a lower count of photons, that carry a lot of energy that is wasted when the plant has to condition those photons.
White LEDs work because the majority of photons created are in the high wavelengths. More red the better. Those hitting their plants with 3500k CCT on up past 6000k CCT are just making their plants work more for less.
Higher CRI results in more red photons. Less heat for the plant to manage. So far my Vero 29 3000K CCT 80/90 trials have shown me that the higher CRI is much better for growing.