Women (under "not much is known..."):
Each game
Of Chess
Means there's
One less
Variation
Left to be
Played

Men (under "their mother cried..."):
Each day
Got through
Means one
Or two
Less mistakes
Remain to be
Played

(under "I can't forgive...")*
She said
She could
Not forgive

Women (under "He tried to explain..."):
He did explain
How things had been
He tried and
He tried in vain
No words of his
Could mollify
The old queen

Basses (under the same part):
He tried
In vain
Longed to
Explain
One died
So that
One could live

Men (under "and so he asked"):
He asked
Wise men
Had to
What on
Earth he
Should do

Unison: "using model soldiers..."

Women (under "chess displayed no inertia..."):
Each game
Of Chess
Means there's
One less
Variation
Left to be played

Men (under "next the Arabs refined it..."):
Each day
Got through
Means one
Or two
Less mistakes
Remain to be made

Women (under "Still further west**..."):
West** and
More west
Chess moved
Progressed
Seemed like
The world
Had one set each

Men (under "once in the hands..."):
The Renaissance
Gave Chess
The chance
To reach
Parts most
Games do not reach

Each game
Of chess
Means there's
One less
Variation
To be played

(Unison "king and queen and rook...")

Women (under "and in the end..."):
In the
End we
See a
Game that
Boosted
In the
Heart of Persia

(Unison "kind of mind..." through end of song)

*Under "sad beyond belief" the Bass part has notes with no lyrics- I believe Leolo has it right that the lyrics here are "so sad/such grief/beyond/belief", leading into the part I have here.

**The score I have scratches out "West" to replace it with "Yet", making the main line "still further yet" and the counterpoint "yet and more west".