Somebody didn't do a good resonance analysis. The tower was probably driven by periodic intervals of wind near the fundamental frequency, if I had to guess.
Almost all of the video footage is pretty much worthless except for starting about 1:10 here:
Looks like it's probably ringing at a higher harmonic than the fundamental, maybe longitudinal/compressional waves instead of or in addition to a transverse component? Those antennae (or whatever they are) seem to be mostly out of phase, so it can't be purely transverse.