My most likely to be argued with thoughts:
1. The first take off was aborted. Turn up the volume and hear the engines spool up, then hear them be brought back to idle. I can just hear them on the flight deck calling for an abort when they realized they weren't able to maintain steering. That call would begin the idling sequence. If it was not aborted, they would have been in the grass.
2. The issue has nothing to do with the smoke. I agree that it is unlikely that the pilots saw it, however, the real issue, which I don't think anyone has mentioned, is the fact that the aircraft was very nearly a runway excursion. Watch how far off the runway heading they are. They could have just as easily straighten out the nose wheel and gone forward into the grass.
3. I suspect that their first thought was a steering fail of some sort. I am not familiar with the warning systems on the MD-88, but I imagine that if they didn't have any lights flashing at them once they regaining and maintained
