Animal rights might be a more philosophically interesting motivation than concern with, say, climate change both because it's more controversial and because it's harder to sort of trade off with other interventions/solutions. Like with climate change, maybe a random person could, in practice, focus their efforts elsewhere more productively. (I'm a vegan but I fly a lot, so my carbon footprint is far larger than even the developed world average; I could make a bigger impact in that regard by just flying less than I do by being vegan.)

With animal rights or welfare, not engaging in or supporting specific uses of animals seems like the most obvious thing that one can do to promote or respect these values (but if papers like this are right, maybe that's an illusion!).

It's a definition. Philosophers label stuff all of the time.