With most AM stations, the tower itself is the radiator. That's the reason for the insulation from ground. If the tower were grounded, it would not be able to transmit a signal at all. In the video, while that cable is attached, the tower cannot transmit.

I wasn't sure about the device they were shorting so I asked the chief engineer for several large radio stations in the area.

That device is a lighting transformer [1][2] -- it allows AC power to be coupled to the tower, to power the lights, without a direct connection, which would severely impact the tower's ability to radiate RF energy. The two little balls is called a lightning gap, it gives lightning a path to ground, other than the connection to the transmitter, since the tower itself is not grounded.

[1] http://www.austin-insulators.com/radio/xfmr.html

[2] http://www.sonifex.com.au/?media_dl=3300 (PDF)