I am very sceptical. They provide a link to a paper by Tadeusz Bałaban about the nonlinear sigma model on a lattice. So I assume that they may have been able to prove that the lattice approximation to the YM theory is consistent.
This approximation uses a discrete grid of points in space-time and it breaks Poincare invariance. The actual YM theory is defined in a continuum. The Millenium Prize specifically talks about R^4, not a discretized lattice.