"Differential Input Voltage" of "Fully Differential I/O Audio Amplifier" (OPA1632)
I thought that differential input voltage = \$V_{IN+} - V_{IN-}\$.


It does but if you are using a circuit in its linear operating area then the voltages on both inputs (due to negative feedback) will be the same. In other words, don't use it as a comparator with hard voltage sources.

Here's a simplified schematic of this type of device: -



It's likely that if the diff input voltage were too great you'd stand a chance of excessively reverse biasing one of the BE junctions at the input stage. It could also be that protection devices (not shown above) will also be present that may restrict the diff voltage.