In that paper, the LEFT-ARC transition from Nivre's arc-eager transition system is added to a list-based parser.
the goal of that transition is different from ours (selecting between projective and nonprojective parsing, rather than building some arcs in advance) and the approach is specific to one algorithm while ours is generic -for example, the LEFT-ARC transition cannot be added to the arc-standard and arc-eager parsers, or to extensions of those like the ones by Attardi (2006) or Nivre (2009), because these already have it.