I've seen this video before, it'* a new weapon system that hasn't been fielded yet. The round is fired using a conventional case, sort of like the old Shillelagh 152mm missile system from the Sheridan and M60A3, or the Copperhead from the M109 Paladdin. It is supposed to go out a set distance before igniting the booster rocket to increase speed, range, and allow greater manuverability before the terminal guidance phase. The second explosion are spacers that keep the round properly aligned in the barrel being blown free to reduce air resistance.
The smoke ring will happen with almost every kind of gun, rifled or smoothbore, simply because it is IMPOSSIBLE to completely seal the tube with the round, and a small amount of the propellant gases will escape past the seal ring before the round begins to accelerate down the barrel. Watch a Civil War era Napoleon smoothbore being fired, and you'll be able to see it in real time, thanks to a sloppy fitting round. That'* why they have that distinctive "chiff-POW" sound.
As far as tracking the missile with a camera like that, it isn't hard. You track the round using radar, laser scanning, or even visually with a good fast computer tracker. You don't turn the entire camera to track it, just the much smaller and lighter final lense box, rather like a periscope. Or it could be a strip of cameras that trigger as the round goes past, sort of like they used for the "bullet-time" scenes in "The Matrix" and "Swordfish".

great explanation, thanks!