The data sheet page 1 states: " The fully differential X, Y, and Z input interfaces are operational over a ±2 V range operation". This a swing of 4 V p-p.
The detailed specs on page 3 show: Differential Voltage Range, Differential, common mode = 2.5, 2 V p-p.
Which is correct?
I assume that 2 V p-p means +1V to -1V on the differential inputs, +1V differential = 3.5V on V+ and -2.5V on V- (with 2.5 V common mode)
The spec isn't +/- 2V per pin, but rather +/-2V (differential) per interface. Figure 3 really tells the tale here.
The specs table, as you mention, is correct. 2Vpp differential w/ a 2.5V common-mode, means one pin is going to +3.5V while the other is going to +1.5V.
My point is that if the differential voltage can be +2V to -2V, that is a total swing of 4V (or 4V peak to peak NOT 2Vpp)