Article I set the VOUT_COMMAND register on the MAX15301/MAX15303 to 0x1334, but when I read it 5 seconds later it returns a value of 0x1333. Why does this discrepancy occur?

The MAX15303 and MAX15301 will “round” the command values to the closest achievable setting. This was a conscious design/definition decision, as the difference between the desired and set values are very small. The LSB should be ~625μV with some offset.