I think the 'effort' being described in the article—despite using analogies of overgripping and physical strain—is mental effort.
When the rabbit has escaped, he returns quickly to a relaxed state. A typical human reaction would be to continue to worry about the predator, to form plans to rid the whole _world_ of all predators, to build a fortress with grass to eat on the inside...
This whole saying that "Nature is red in tooth and claw" is overstated. Most animals have normal, humdrum days like we do.
However, I think it was the Buddhist teacher, Ajan Cha who said: "We live in a world where we must eat to survive, and some of us are uncomfortable about being eaten."
But this does not mean that every animal lives a life of unremitting terror all the time.
I’m wary of your use of 'romantic' as a descriptor here. It's a rhetorical shortcut which makes it easy to pre-emptively dismiss a position as naïve without further examination.