So I spent a little longer looking at the video with it paused. That trailer right next to the crane, has the rear outrigger box on it, its the yellow upright box with pins in it- that I first thought was a winch frame.
So to get down to a legal weight, they have to pull outrigger boxes off (at least the rear one it looks like). Then they either use that crane with the suspension locked, or a assist crane to install the outrigger boxes. I don't know which procedure that crane has, but either they need to scope in boom when bringing it out of dolly, or the suspension didn't lock up like it was supposed to.
Most 300 and up have front and rear removable boxes. The 360 ton I was around had them, the front boxes are a pain to remove, the back one is pretty easy.