The LFS replays are not videos, but the data that comprises of the movements and actions of the vehicles and racers.
If anyone wanted to make a replay program, they'd basically have to make LFS all over again, or actually run LFS and embed the LFS window within it's own.
Edit: or, as AlienT says, you could record them from LFS, using fraps or something similar, and then play them using any old video program.