> If the quantity appears in equations, I find it hard to believe that it was never given a name.
It does have a name: mass!
What I'm skeptical of is that this "stiffness" is somehow logically or conceptually prior to mass. Looking at the math, it just is mass. The term in the equation that this author calls the "stiffness" term is usually just called the "mass" term.
> it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field"
If you are referring to the claim in the article that goes along with the equation E = m c^2, that claim is the author's personal interpretation, which I don't buy. The mass appears in the dispersion relation whether the particle is at rest or not. "Rest mass" is an outdated term for it; a better term is "invariant mass", i.e., it's the invariant associated with the particle's 4-momentum. Or, in field terms, it's the invariant associated with the dispersion relation of the field and the waves it generates.
But it's not really just "mass", it's "characteristic mass of stationary minimal possible wrinkle in a given field". And it doesn't sound like it has anything to do with force range, and "stiffness" does.