It would be my guess that physics system is in place only to add to the realism of the game. As we can see from the video, debris falls and lasts only for a few short seconds. In the scene where the warp rays are fighting the marines, when the debris from the far left warp ray falls, the marine doesn't appear to be blocked by it. This would be a good idea, but implementing the debris structure and such would be difficult. This too would be the case for debris damaging units. In the beginning when the zealots are demonstrating their charge on the Terran barracks, we see the structure explode but no zealots are damaged. If such damage were to occur, this would be one of the moments.

One question I do have is at the end of the Gameplay Video when the Protoss and Terran are in their final battle. We can see zealots and immortals running over environment that appears to have holes and ruined structures, but when the ghost's nuclear launch blasts three giant holes in the environment, are units still able to move over it?

Edit: After watching the scene again, we can see 2 ghosts walk right over the debris from the nuclear explosion. A few seconds later we see the hole disappear into the previous terrain and that is when the zerglings attack. I think it is confirmed at this point debris will not play more than a visual feature in StarcraftII.