They prove a new upper bound to a combinatorial quantity that controls the worst-case running time of an algorithm of Dadush, not an upper bound to the optimal value of a given ILP instance.

If they wanted to see their ideas work in practice, they could implement Dadush's algorithm in light of these new bounds, but this would be unlikely to outperform something like CPLEX or Gurobi with all their heuristics and engineering optimizations developed over decades.

Otherwise, and this is the sense of the quoted sentence, they could go deep into the bowels of CPLEX or Gurobi to see if their ideas could yield some new speed-up on top of all the existing tricks, but this is not something that makes sense for the authors to do, though maybe someone else should.