Just figured it out, hopefully this will help someone else in the future.
Of the needed pins for the DB9:
Uₐ₀: absolute reference signal, corresponds to Z on the Sino pinout,
Uₐ₁: Square wave 1 signal, corresponds to A on Sino,
Uₐ₂: Square wave 2 signal, corresponds to B on Sino.
Of the other pins:
U̅ₐ̅₀̅: inverse of Uₐ₀, unused by Sino,
U̅ₐ̅₁̅: inverse of Uₐ₁, unused by Sino,
U̅ₐ̅₂̅: inverse of Uₐ₂, unused by Sino,
U̅ₛ̅: fault detection signal, unused by Sino,
0V Uₙ: duplicate of ground, appears to be unnecessary based on Heidenhain note,
5V Uₚ: duplicate of common, appears to be unnecessary based on Heidenhain note.