Is it normal for the flaps to move like this?
I believe the engine is mounted in front of that part. 

This means that if the part moved along with the rest of the spoiler the jetblast would be deflected down which will create an upward force on the wing. You don't want that while you have full spoiler deployment.

Putting a gap in the spoiler will reduce stress on the full spoiler from the jet blast. This leads to less expensive maintenance as the stresses are reduced mostly to a single panel and its attachment points.

As @Ron points out the flap geometry is such that you can't have the full flaps adjacent to each other without them jamming up when they deflect. Putting an extra panel between them lets it move on top of the other 2 flaps when necessary.