8.01 deals with preliminary movements before the pitcher lifts his leg. The post says the pitcher "lifts leg towards third" - agreed that if he started home with left leg (or umpire judged first movement to be even close to going toward home) it is a balk but that isn't what was described.
Disagree again. The pitcher was in "the stretch", preliminary movement, when the runner broke to 3rd therefore Rule 8.01 applies.