IF it was a real door .... I suspect the door isn't physically linked to a computer linked to twitter.
Those doors tend to have two states - open or closed. So I guess they have to manually press a button to start and stop it in steps. Then they record that process as a series of videos, one for each phase. Then it's a simply thing to have a flash animation that animates the door opening as the twitter count hits each target.
Having written that, it occurs to me that it's probably an animation entirely constructed in photoshop (or similar) without any video. Take a closer look at it, that's not a real door with real light and real texture, its a cartoon.
I also notice they haven't defined how many tweets are needed to open the door. The cynic in me thinks it will open in small increments over an hour regardless of how many tweets happen.
