mangue: The pawn rule is a part of the draw rule for regular chess: the game is declared a draw after 50 moves without neither a piece capture nor a pawn move.

This rule should be seen as an extension of the more easily comprehensible 3-times-repeated-position rule. The idea is that after 50 moves without an essential change to the board nothing more is likely to happen. The pieces are just dancing around.
So why the pawn clause? because a pawn move IS an essential modification: it is not reversible.

By the way, for regular chess the debate about this rule is still open, because there are endgame position which are known to be won, but the way to the win takes more than 50 moves. For example, K+N+N against K+P.

Whether all this is pertinent to dark chess is another point.