I'm not an expert, but my understanding was that this is mostly a theoretical result, similar to finding a new lower bound on matrix multiplication. As far as I know, all BLAS implementations use the O(n^3) matrix multiplication algorithm even though a O(n^2.37) algorithm is known because the O(n^3) algorithm maps much better onto hardware and has lower constant costs. I don't know as much about it as I do matrix multiplication, but I believe linear programming algorithms are in a similar state, where the simplex algorithm has exponential worst case, interior point algorithms have polynomial worst case, but both methods are used in practice.