The handles of the gizmos are in different location than they are rendered. The gizmos are rendered on top of the object’s pivot point, as they should be, but the handles can’t be grabbed and moved from there, instead, to grab the gizmos, I need to put the cursor to the left of where the gizmo (when looking from the Z axis) is drawn to grab it and move it around.
See this video. Note that while in the video I use a static object, the same happens with movable objects, except the objects actually follow the gizmos.
Using UE 4.8.1. Also running on an AMD card, if that makes a difference.