lol
Why chess is not like war

I think that chess is not necessarily comparing itself to war, but more a representation of a battle.
In your first point, "1. Clausewitz reminds us that "War is the province of mistake." The history of warfare is replete with battles lost by simple-minded mistakes. Thus, it's more reasonable to expect a mistake from the enemy in war than over the chessboard." - It is thought that a perfect game of chess would result in a draw, therefore the losing side is the first to make a mistake (or at really high levels a bad inaccuracy) or even the person who was not last to make a mistake.
Your second point, "2. Clausewitz also coined the expression, "the fog of war", to express the confusion and lack of information that is common to all battles. There is no such fog on the chessboard--all of the opponent's pieces and maneuvers are visible. Once you've lost a piece, your opponent doesn't have to worry about hidden forces or a suddenly introduced secret weapon." - I would compare this fog of war with an extremely complicated position where it is very difficult for either side to, 'see' a rivals plan or even form one themselves
"3. Over the chessboard, a single piece is a far larger part of your total forces than a single "aircraft carrier". If you reduce everything to its equivalent in Pawns, you start with 39 units. So being a piece down is having a loss of about 10% (or more, if it's late in the game) of your total fighting force. In a war, loss of a unit can be recouped, given time; you can produce more hardware, recruit and train more fighters. This is absolutely not the case with chess." Yes this is true although pawns can be promoted to other pieces, 'reinforcing' your, 'army'
4. Modern war is no longer fought as it was in the 1500s-1700s. Back then, war was a contest of kings and would end when one side conceded some piece of territory to the other. Frequently, modern war is seen as a struggle for survival by at least one of the sides. Thus, the stakes are incomparably higher than a chess game, where all losing costs is a blow to your pride or maybe some money. This justifies continuing a struggle much longer. - Although chess was first played a very long time ago, way before even a concept of modern warfare
5. A chess piece cannot be told to hold on a little longer, until the relief column arrives. A man can, and depending on the degree of his belief in his command, he may hold even beyond the point of sanity. Going back to an earlier point, there are no relief columns coming, unknown to the enemy, on the chessboard. - I suppose it could be said that a piece trying to distract a king to one side of the board in an endgame whilst you try to promote a pawn could be considered a similarity.
I'm just posting my thoughts on what I considered an interesting and well written thread, I would consider chess to be representative of a war/battle although perhaps it should be noted that, (sourced from the book, 'the immortal game') although Napoleon was, 'really good at war', he was, much to his own annoyance, not very prolific at playing chess

If there has to be a dozy analogy, I'd liken chess to a lesson rather than a war. Of course, the best fun is when the teacher and student positions are blurred by their close proximity; then we have two colleagues, pretty much on the SAME SIDE, discussing ideas. "what if...x...", "No, no,... then y, surely...", "but, hang on, what about this..", "yes but then, that...", "O.K. plan B...", "Ah!..."
Two brethren have bothered to make themselves experts and the chess game is a detailed discussion, friendly and delightful, of their ideas.
Where is the war?

Yes aadaam your right and I don't think I've seen it better put but I meant my points to show that it is perhaps representative of the tactical and strategical thinking relating to a battle, but meant to be played in a friendly environment. However, one could be fooled into thinking otherwise when the history of all the underhand methods employed by some players. However I feel that in just about all cases it is as you put it, 'a lesson' that anyone of any age and any skill level can learn from.

Having bought 'The Art of War' by Sun Tzu, it's interesting to note the overlap. Chess very much is a war-like game.

A piece can't "kill" another piece while remaining on its own square as if it were an archer. If that were true, then I'd find chess far more confusing.

A General has to "re-use" his remaining troops in the next battle, a chess player always starts with his full army again.
No sane General would exchange troops just to "simplify" the battlefield.
And we're not even thinking about logistics, troop psychology, politics etc. (I don't have to worry about my pawn getting scared and running away, a Government deciding that I only need 6 pawns or making sure my chess set is well fed and paid before each game)

I played a French guy the other day and he surrendered before move 20, so I guess chess is a lot like war.
Seriously great post by the OP, I enjoyed reading that. And the rebuttals were interesting. I couldn't come up with anything of substance myself so I resorted to making a bad joke as stated above.
Everyone knows that chess is historically compared to war.
Here is a bunch of reasons why this comparison should not be taken too seriously. I am not the author, it was found on the web.
Enjoy.
1. Clausewitz reminds us that "War is the province of mistake." The history of warfare is replete with battles lost by simple-minded mistakes. Thus, it's more reasonable to expect a mistake from the enemy in war than over the chessboard.
2. Clausewitz also coined the expression, "the fog of war", to express the confusion and lack of information that is common to all battles. There is no such fog on the chessboard--all of the opponent's pieces and maneuvers are visible. Once you've lost a piece, your opponent doesn't have to worry about hidden forces or a suddenly introduced secret weapon.
3. Over the chessboard, a single piece is a far larger part of your total forces than a single "aircraft carrier". If you reduce everything to its equivalent in Pawns, you start with 39 units. So being a piece down is having a loss of about 10% (or more, if it's late in the game) of your total fighting force. In a war, loss of a unit can be recouped, given time; you can produce more hardware, recruit and train more fighters. This is absolutely not the case with chess.
4. Modern war is no longer fought as it was in the 1500s-1700s. Back then, war was a contest of kings and would end when one side conceded some piece of territory to the other. Frequently, modern war is seen as a struggle for survival by at least one of the sides. Thus, the stakes are incomparably higher than a chess game, where all losing costs is a blow to your pride or maybe some money. This justifies continuing a struggle much longer.
5. A chess piece cannot be told to hold on a little longer, until the relief column arrives. A man can, and depending on the degree of his belief in his command, he may hold even beyond the point of sanity. Going back to an earlier point, there are no relief columns coming, unknown to the enemy, on the chessboard.
6. Even in war, there comes a time to acknowledge defeat, and save as many lives as you can. Ancient military saying: "Always reinforce victory, never reinforce defeat." If a plan has failed, do not keep feeding troops into the chopper. Over the chessboard, this translates as not continuing a clearly lost game but conserving your energies for a possible win.