I worked on this system back in the 80s. It was called SACCS and it had been installed in 1961/62. Rumor had it that it was the first computer system in the military to use transistors. It had racks and racks of drawers full of cards with discrete components that could be replaced via soldering by the front-line (so to speak) maintenance people. It communicated with huge modems, over dedicated lines, that featured mechanical resonators and was capable of 2400 bps. It used core memory (I still remember - X, Y, sense, inhibit). Some components were notoriously difficult to fix, so we were told if it's working, don't mess with it.
In the 70s, the IBM Selectrics that functioned as input/output devices were upgraded to black and white VDUs. It had a tape drive that used 35mm magnetic tape that could be a bear to keep working.
In 1988 or so, at least at most of the bases, it was upgraded to SACDIN. A single rack of more modern (for the time) equipment to replace the whole room-full of ancient stuff.
It's not all that surprising to me that it's still online. The acquisition cycle for things like that takes forever, and with mission critical things there's that whole if it's working, don't mess with it thing.