Almost certainly howitzer fire. One has to remember that because of the (possibly) high trajectory of the projectile, that it can be in the air longer than it takes for the report of the gun to travel to the target. It really depends on the range and angle of fire, though. The thing that makes me wonder about the authenticity of this clip is that the rounds land one at a time, and it looks like some editing has been done in between rounds. In my day we didn't fire CB one round at a time.
I don't pretend to know what current doctrine is, but in my day we would have fired at least a platoon-1 on a target like that, more likely a whole battery would fire. That means that no less than 4 tubes (and more likely 8...) would fire simultaneously on a given target in order to cover the target area as much as possible, considering error probabilities and such. As far as accuracy goes, those shots weren't that bad for initial, unadjusted rounds. With an observed adjustment, a second volley could spoil the entire day for anyone out there, but then again, counter-battery fire isn't always observed unless you've got eyes in the sky somewhere. Most of the time it's fired at locations triangulated from radar observations, i.e., radar sees their rounds in the air and then a location is calculated from two or more such observations.
I don't doubt that the impacts are real, but I'm guessing that this was staged as a training film for the... er... target audience.