Do you also object quarks and gluons having "color" charge?
Mass is a bad term because it's loaded with so many meanings and equivalences already. But also in the kindest and most accurate reading here it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does, which was the whole point of the article.
> An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
They do, there are 3 and they add up like primary colors, so all 3 make stuff colorless. That's why those names were chosen. Because of similarities with color we know from color theory.
> there is no such thing as what this author calls a "floppy" object
It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope because nothing holds remote parts of the rope in place. The only way for a wrinkle to exist in such rope is to travel at "rope speed". If there's stiffness then a wrinkle can travel at any speed or none at all, because it can oscilate without moving, which is rest energy (mass). So it explains all bosons.
What's great with this analogy is that it coveys that both mass and force range arise from a single term of the equation. There's really no causal connection between them. Neither limited range causes mass nor mass causes limited range. They both come from a single intrinsic field "quality".
There's also no anti-blue color in color theory but it's easy to imagine it so you can intuitively understand its behavior.
> It's easy enough to imagine as an unattached rope so pulling at one spot affects the whole rope
Not instantly; the force you apply at one point still has to be transmitted through the rope. And if the rope is unattached and not taut, it won't transmit force well at all, and you have very limited control over how the rest of the rope will move when you pull on one part.
I don't see how any of this is a useful analogy to how massless gauge bosons work in forces like electromagnetism.
> Do you also object quarks and gluons having "color" charge?
No, because no physicist tries to argue that "color" is an appropriate term because of some physical interpretation that involves actual physical properties of colored objects.
This author, OTOH, appears to be arguing that "stiffness" is a better term than "mass" because of some physical interpretation that involves actual physical properties of stiff objects. An analogy with quarks would be to argue that "color charge" is an appropriate term because red, green, and blue quarks somehow have actual properties associated with those colors.
> it still doesn't naturally lead to explaining why some forces have limited range the way that term "stiffness" does
I'm not sure the explanation of that in terms of "stiffness" is any better, because in the setting where the term "stiffness" comes from, there is no such thing as what this author calls a "floppy" object. So his explanation only "explains" the behavior of forces associated with massive gauge bosons at the price of throwing away an explanation of the behavior of forces associated with massless gauge bosons.