This is not a complete answer, but maybe it will inspire somebody to find one.
There is a parallelism between the two stanzas, especially in the last half of the stanzas. Here is the last part of the two stanzas lined up, with corresponding lines next to each other.
. . .
Songs of the glory and gladness of life, In blowing forests and breaking tides,
Of poignant sorrow and passionate strife, In the happy laughter of new-made brides,
And the lilting joy of the spring; And the nests of the new-born spring;
Of hope that sows for the years unborn, In the dawn that thrills to a mother's prayer,
And faith that dreams of a tarrying morn, And the night that shelters a heart's despair,
The fragrant peace of the twilight's breath, In the sigh of pity, the sob of hate,
And the mystic silence that men call death. And the pride of a soul that has conquered fate.
"Of hope that sows for the years unborn," corresponds to the line "In the dawn that thrills to a mother's prayer," both lines being about hope for the future.
"And faith that dreams of a tarrying morn," corresponds to the line "And the night that shelters a heart's despair," both lines being about keeping faith through a dark time.
So if we believe the first stanza corresponds roughly line by line to the second one, "the pride of a soul that has conquered fate" should correspond to "the mystic silence that men call death."
I would hazard that "conquering fate" means something like coming to terms with your eventual death, but it's quite possible that I don't know enough about Indian philosophy to really analyze this poem completely.