It goes deeper than just 8-inch floppy disks to operate our nuclear arsenal. We're talking arcane 56 year-old computer code that's used to generate your tax return at the Department of Treasury and Common Business Oriented Language from the 1950s keeping track of benefit claims being filed and dates of death for the Department of Veteran Affairs. Unlike the DoD's prehistoric floppies, these latter two issues have no defined plans for replacement or modernization.
There are a few things to take away from this. For starters, some of these old systems are almost assuredly very susceptible to intrusions. But, like Ars Technica
notes, a few have been augmented with comparatively modern bits and bobs. The problem there is that even those "upgrades" have been abandoned in terms of support as well. There's no quick fix here, or, more likely, a fix at all, especially with how slow the wheels of bureaucracy move.