That's not how it's written in the post though. If you just swap out the "inertial mass" at the end and the "rest energy" somewhere in the middle it makes more sense:
> because photons have rest energy (=> kinetic energy) that can be viewed as mass in special relativity
> [...]
> impact the gravitational field despite having no inertial mass (=> rest mass)!
Speaking of "mass" in context of relativity is always a bit tricky. The term "inertial mass" for example is really saying something about how an object behaves under the influence of a force (F = ma), not how it behaves relativistically (that would be "relativistic mass", E = mc2).
Maybe you could write “because photons have energy that can be viewed as (relativistic) mass” then. Or maybe he did really refer to the “rest energy” of photons? That seems weird even for an experimentalist ;-)