How do some instrumentation amplifiers handle such wide common-mode input voltages?
They're drawing a rather large current- 25uA from each input typically, that's enough current to power the high-side switches provided the chopping isn't too high frequency. It's probably something like 100kHz. 

So the components exposed to the 80V would be the capacitors and some kind of high voltage current sinks, possibly lateral JFET type structures, maybe someone with high voltage monolithic IC design experience can comment.