I believe you can actually do that with the vehicle model itself.
All cars have 'Damage' versions of their parts. So when you damage something like the door, the model for the door gets replaced by the damaged version of said door. All you'd have to do is take it to the next level.
I remember using an enter-able bus mod years back now, and it done the same thing by making the damaged parts cover more of the vehicle, so for example if I smashed the side of the bus, there would be broken windows and dents and all sorts of cool damage models on the side. But the point being, I believe you can do this by modifying the actual vehicle itself so it has those damage effects.
I think you'd have to put the damaged parts as a child to the damaged vehicle part. So for example if I wanted to make the whole front of a car have a damage effect like the one in that video, I'd make a 'damage' version of it and link that model to the damage bumper model as a child to it in the hierarchy.
I'm not 100% sure on this because it's been a long time since I've actually done it, but hopefully that will give you a good idea on how to achieve these effects for vehicles in GTA SA.