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To clarify, Glinski's pawn capture does not advance the pawn one step
closer to promotion as in regular chess.  It advances the pawn 1/2 of a
step closer.  In my variant, a pawn capture advances the pawn 3/2 of a
step closer, so neither variant emulates regular chess perfectly in this
regard.

The diagonal pawn capture used in my variant allows pawn chains to behave
as they do in regular chess, which is not true of Glinski's pawn chains.

For example, it is impossible in Glinski's chess to have interlocking
head-to-head (blocked) pawn chains where the pawns can't capture each
other.  Try creating something equivalent to the following regular chess
pawn chain:  White pawns on f3, e4, d5; Black pawns on f4, e5, d6.  All 6
pawns are immobile, they cannot capture each other, and each side forms a
protection chain starting at an unprotected base pawn.  In my variant,
the
equivalent would be White pawns on g4, f6, e7; Black pawns on g5, f7, e8.

In Glinski's variant, it can't be done:  Either the pawns can capture
each other, or the pawns on each side don't form a protection chain. 
(Note:  I am labeling hexes using the bent-rank notation where the 1st
rank consists of the 11 hexes on White's edge of the board.  The hex in
the center of the board is f6.)