Hoover,
The move is called an inside move. As you explained it, it is not a balk. Reiterating what Coach2709 said, he disengaged, he became an infieder.
We will typically use an inside move for the following: (for those that don't know and inside move is only used at second base)
*you think he might be stealing
*you think the hitter might be bunting (it is informative)
*runner doesn't honor that fact that you can inside move him (ie, he gets his secondary as soon as pitcher lifts his leg....just a way to keep him honest)
You don't have to throw the ball to second or third ever.....
In the examples given you don't throw either....except in the case you explained.....