I'm sure that what RPD was referring to was the ability in Fed to stay engaged on the third to first move. In NCAA and OBR you required to break contact on the move to third. If you stay engaged the move to first is a balk. In Fed you may make the feint to third, stay engaged and throw to first. If you stay engaged then you must throw.
In the OP the pitcher stepped over the back toward second, stepped off, took a few steps and then threw to third. This is perfectly legal. Once he desengaged he is a fielder and may do what he wants.
If the runner breaks early enough, the pitcher step directly to third and throw.In NCAA and OBR he may do this to play on a runner stealing. In Fed he may do this to play on the runner or drive him babk.
The big difference is in Fed it only has to a break more than his lead. In NCAA/OBR it has to be more, a ligitament attempt to advance. I am in the halfway or better to determine this. It is a rule of thumb and not a "must do" measurement.