The researchers might have conducted a parallel study while carrying out this research. They could have hired two graduate assistants, telling each of them that they would be paid $100 at the end of each day's research. And then, at the end of each day, they could have paid the first assistant, but not the second -- not the underdog. My theory is that the underdog would quickly become "less and less inclined" to continue showing up for work.
In the case of these hypothetical assistants, of course, no one would mischaracterize the unpaid underdog's response as "envious." She might be angry, but she'd be refusing to cooperate not because she's jealous of the other assistant, but because she is the victim of an injustice -- because the situation is clearly unfair. Her response is not motivated by envy but by a sense of justice.
The Times and National Geographic reports on the actual study do not allow for the possibility that a similar motive is at work in the dog's response. They don't seem to recognize the significant and crucial distinction between "angry at unfair treatment" and "envious." National Geographic stumbles toward a clarification, conceding that "this kind of envy" is "really an aversion to unequal reward," but then their article goes right back to using the word envy as though these two things were reliably interchangeable.
This particular confusion is, sadly, quite popular. We hear exactly this same bit of madness almost constantly from apologists for irresponsible wealth. Express any concern about inequality or about the plight of those who have less than the minimum amount they need to get by and they will say you are guilty of "the politics of envy." Try to explain the distinction and they will, in turn, explain that they understand what you're saying, they simply reject it. "Justice," they will insist, is simply a polite euphemism for disguised envy. The virtue is just a mask for the vice.
It's not surprising that they would argue such a thing. Of course they don't believe there's any such thing as justice in this life or any other. That's what they're banking on. Envy they accept as real. Justice they regard as mere superstition.