This possibly in reference to a:
Which is a:
Chess opening that can gain an surprising and unexpected advantage (likely at the sacrifice of a few pieces in the long run) which involves moving the bishop before the knights, passing "Blessing" a few pawns on the way toward the center of the board.
As stated on Wikipedia:
"The Bishop's Opening is one of the oldest openings to be analyzed; it was studied by Lucena and Ruy Lopez. Later it was played by Philidor. Larsen was one of the few grandmasters to play it often, after first using it at the 1964 Interzonal tournament. Although the Bishop's Opening is uncommon today, it has been used occasionally as a surprise by players such as Kasparov"
Some correlations:
The old cardinal, in his stature, was listened to. He went to Danton’s regiment, then to Édouard’s regiment, and blessed them.
"Danton" and "Édouard" are probably in reference to columns "d" and "e" on the chess bord, so Danton and Édouard's "regiments" are probably in reference to the pawns at "d" and "e" that the bishop must pass and "bless".
Then, another came and blessed the other army. Or he would have, if he wasn’t stuck behind another regiment.
This is probably in reference to the other Bishop that is suck behind the other pawns.
Then, he could finally move, and the battle began.
This seems to be a variation of the Bishop's Opening that involves moving both Bishops before any captures are made or "Battle".
Danton struck down some men of the other army…
The pawn at column "d" made a capture.
But Sir Birch charged.
"Sir Birch" is probably the Knight at column b: "Birch" for "b" and he is a "Sir" hence the "knight"
Danton was the only one who survived
In this scenario, the pawn that originated at column d was the only piece that advanced which was not not captured.
Now as for the question:
Why did they have to die?
The simple answer is "to win the game". There obviously many ways the Bishop's Opening may play out, but almost all of them involve sacrificing at least one pawn (but sometimes a few). It is a necessary sacrifice to gain the advantage and put the opponent in check, usually with the "Blessing" of the Bishop (the Bishop is used to put the King in check).
As for the Title:
The Seventh Seal
The Seventh Seal is a movie from 1957 in which "A knight returning to Sweden after the Crusades seeks answers about life, death, and the existence of God as he plays chess against the Grim Reaper during the Black Plague." (IMDB)
And you probably guessed it:
The knight plays a Bishop's Opening.