Hi,
First important thing is: it is a delta sigma ADC, which has very unique step size (low DNL, low INL).
Then - only with low input signal - they use half or quarter of the usual reference:
* 1.25V or 0.625V instead of 2.5V. Therefore the the full range input is only 1/2 or 1/4 of the usual range, but the digital value is multiplied by 2 or 4 (= shifted 1 or two buts left)
* to compensate for the left shift they shift the digital value right.
This just means that the digital value does not alter, but the accuracy is improved.
******
The usual way is to amplify the input signal to fit it to the ADC input range, then afterwards the software takes care of the increased digital value.
The Maxim solution has the benefit, that there is no need for an external amplifier, and the software doesn't need to compensate for the modified digital value.
Klaus