About 30 seconds into the video there is an aircraft off to the right with no contrail behind it.
Contrails only form when the moisture level of the air at the altitude the plane is cruising at is near saturation. Add the water vapor from the exhaust and a few particulates, at low pressure and temperature, and it will condense into an ice cloud. Missiles don't leave 'contrails', they leave trails of combustion products (smoke) which aren't dependent on atmospheric conditions or altitude. The video clearly shows a column of smoke, its source is accelerating away from the camera to about 20 or so degrees right of the viewer's zero.