As someone else pointed out, this statement is meaningless with only half of the nuclear-armed nations on the planet participating. Even a relatively minor nuclear exchange between any of the smaller nuclear powers would wreak havoc on the rest of the world, and I'm not referring to side effects of nuclear detonations. Stock markets would immediately crash and a global economic depression would ensue, although I doubt it would last as long as the Great Depression of the 1920s. Beyond that, imagine the resulting massive humanitarian crisis that would cost billions of dollars and require global cooperation on an unprecedented scale.
They're also not saying anything that they haven't already known for decades. It would be no different if Facebook, Twitter, Microsoft, Apple, and Google all released a joint statement saying that operating systems and applications tracking users is unethical. Really???? Who knew? Everyone knows you can't "win" a nuclear war. Oh, you might suffer fewer casualties or fewer cities destroyed than your enemy - but would the resulting devastation be worth the technical "victory?"
MAD only works if the leaders of all countries possessing nuclear weapons are rational. During the mid-20th century, we were fortunate that this was the case, more or less. Now, we have delusional megalomaniacs and theological fanatics in possession of these weapons. Rationality is no longer protecting us - only luck is keeping the nuclear genie in the bottle right now.
Make no mistake: nuclear weapons will be used in combat within our lifetime. It is a statistical certainty. The only questions are when, where, who, and how many?
Maybe that's what it will take for the human species to finally wake up. But I doubt it.