Why do these washers agitate a little before doing the draining? Check out the video. It agitates a little before draining at 0:15 to 0:17

I think it is somthing to do with the transmission. The transmission spins in the spin direction and after about 35 clicks of a gear wheel, the entire transmission locks up and does not move producing a neutral drain. When the machine stops, the transmission unlocks and locks the agitator so it spins with the whole basket. This is why the machine does a spin-out drain if it is stopped during the 2-minute-long drain cycle. The agitator moves at the start of drain because that is before the transmission locks. At the end of drain when the transmission actually unlocks you can also see the entire basket jerk slightly. This is why those machines make the thunk sound as the start of drain when the agitator moves. You can also hear it go thunk at the end of drain after the motor completely stops.

Uhhh, not exactly.

There are a couple agitation strokes at the start of drain because the transmission is still engaged in agitate mode for a moment when the motor reverses, until the gears disengage. The agitator does not lock during spin or drain. One can grab hold of the agitator during spin and hold it still. The basket may turn a bit at the end of drain if the clutch engages a moment before the motor coasts to a complete stop during the pause between neutral drain and spin.