It's related to the premise of David Brin's Uplift series, so in one way it's the basis of multiple trilogies of books.
It's been one possible answer for as long as sci-fi has debated the Drake equation and Fermi paradox. Arguably, it is a critical part of the thesis of War of the Worlds as far back as the late 19th Century.
I don't see how. David Brin's Uplift universe is bureaucratic, with interspecies interactions heavily regulated and angling towards preserving, not eliminating life.
Cixin Liu's vision is purely game-theoretic, where anyone who makes noise is likely to be preemptively sniped by someone else, out of pure sense of self-preservation. I don't recall seeing this concept anywhere else.
The implication in the Uplift universe was that the bureaucracy and "gamification" of interspecies interactions was designed to avoid such an elimination state, but such a thing likely existed in its deep past. The thesis, as such, of the Uplift universe was generally that mutual cooperation was hard, but should win in the long run. The emphasis in the hard was that by default most societies wanted to shoot first and ask questions later even with cooperation heavily incentivized by the rules/games.
The Killing Star (1995) would be the main one that comes to mind for me. Even uses a dark forest as a metaphor though in this case it's a city park full of gangsters.
The earliest I remember was by Greg Benford: something in the series that started with In the Ocean of Night (1970s). I think it was that novel, but I'm not sure; but towards the end of the one I'm thinking of, as this picture of the universe was coming together, a character thought of the nighttime sky as like the eyes of hungry predators surrounding a campfire.
(Not to say I think this theory about the Fermi paradox is a very good one.)
At minimum, Revelation Space features it as a major plot-point and was published in 2000, significantly predating Dark Forest.