I just finished reading the book, additionally to seeing the movie previously.
The question has several flaws, which I will try to clarify first, before providing my point of view.
the novel is a metaphor for environmental destruction?
The novel cannot be a metaphor for environmental destruction. The environment is already completely destroyed. Even the author (Cormac McCarthy) states clearly that the past is irrelevant, the cause of destruction is not in the scope of the intention of the book.
The book is about a "place" without any actual environment at all. The book would have been equally valuable if things would have happened on a lifeless planet. The people could be the last survivors of a colony on that planet. The struggle would be the same.
environmentalist George Monbiot claimed ...
Well, George Monbiot is deeply politically involved, as much as the rest of his family (from Wikipedia page). It is their way of life to use or to deform reality to serve their purposes. In the same way, we can claim that "From Earth to Moon" by Jules Vernes is "the most important environmental book ever written". Unless he provides actual reasoning for the claim, we can ignore his agenda when analyzing the book.
my recollection is that it's strongly implied to be nuclear.
The clocks stopped at 1:17. A long shear of light and then a series of low concussions.
I had this feeling shortly also, until I analyzed the "science". There are two types of clocks. Mechanical clocks, just as steam locomotives, are immune to EMP's, therefore they are unlikely to stop. Electronic clocks cannot just stop, eventually they just get fried - and they show no time at all any more. Light and concussions could be a reference to an electro-magnetic storm (thunders and stuff).
Additionally, people who watch nuclear bombs exploding (i.e., directly, not through video recordings), usually do not live long enough to raise children and travel the world southwards by foot in a destroyed world.
... the final paragraph. I won't quote it ...
Not only that you should quote it, you should also point out the parts which are relevant from your point of view.
especially when the author strongly implies the disaster is nuclear
No, the author does not imply such thing.
a warning about climate change
As I said already, the book does not present any climate change. Maybe the climate was like that forever. Maybe the birds and the fish existed, but on the home planet. There is no claim about that either.
So, metaphor or no metaphor?
Obviously, the book is about a journey and about struggle, much like Stephen King's "The Stand". So while "The Stand" is more about the survival after the Apocalypse, "The Road" is in fact a lot more abstract.
This "abstract" nature of the book makes me have the strong feeling that the journey and the struggle in the book ("The Road") are a metaphor of the struggle of people following their life paths in the "destroyed" world of "today".
The gray color in the book is the clear metaphor about the feeling of helplessness and depression.
The lack of animals, birds and plants is a "metaphor" for the lack of life in the cities and metropolises of the world, where the cement, asphalt, metal and glass are definitely hostile to any kind of life form.
The scarcity of food might have two facets: in some parts of the world, the food is literally scarce. In the parts of the world where the food is quantitatively not scarce, the quality of the said food is scarce (GMO, additives, hormones, preservatives, antibiotics...).
The aggression of some people against other people (even good people turn aggressive occasionally) is a characteristic of the capitalistic "color" of the world, where everybody fights for him- / her- self. While association does happen occasionally, it defines less and less the reality of life these days.
The lack of trust in the other people goes hand in hand with the aggression, with the same explanation.
The children in the book are a metaphor for the little and fragile innocence still left in the world.
The woman at the end (unlike the other women throughout the book) could be a metaphor for the chance of rebirth of the world as a better place for everybody. This is especially strong - the rebirth adopts the innocence - or maybe the innocence adopting the rebirth?
And with this interpretation in mind, we come to understand why Cormac McCarthy clearly stated that the cause of the destruction is "not important" for the book. He does not target a single cause of the current state of things. He does not have in mind the most recent, or the oldest. While some causes of the "chaos" today are ancient (e.g., slavery, in all its forms, with their consequences), others are recent (the use of atomic bombs, greediness, lack of empathy and solidarity etc.).
The book is NOT a metaphor for environmental destruction, but the environmental destruction (regardless of the cause) is a metaphor for the world today.