Its a dedicated phone line between the sideline and the box where their coaches sit. I imagine there are a few different ones so the O and D have separate lines. Instead of having to install an elaborate network that involves a PBX or CM, they can just run a copper wire between the phones and plug in power. As long as the headsets stay on the cradle voltage is kept from completing the circuit and the ringer isn't isolated off the circuit. As soon as one of the handsets is taken off the cradle, voltage is then allowed to flow through the copper to the other phone's ringer and it rings.
There is no reason at all to do anything other than what is in the photo. I am sure just about every single stadium has the same set up. It would be a waste of time and $ to do otherwise. KISS.
This is probably more the UT player couldn't tell if it was ringing or not so he put his ear closer.