According to the guy that took the time lapse of the missile each exposure was between 3.5 - 20 seconds each.

"It is a Canon T3 Rebel set up as a webcam. Images are captured about every 40-45 seconds. 3.5/20 second exposure/ 1600iso. I only run it on clear nights or when there could be severe weather."

I'm not sure we would see the shape of a missile even at 3.5s of exposure. It would depend on the distance between the camera and object.

http://www.thedrive.com/the-war-zone/21461/lets-talk-about-that-mysterious-rocket-launch-over-whidbey-island-photo-from-washington