In the first sentence of your original post you make mention of "reading" the DDS via the parallel port. Just to be clear, the parallel port of the AD9910 is "write-only".
The intent of the parallel port is to give the user access to the DDS core for controlling frequency, phase and amplitude without having to write to the SPI registers. This is a valuable feature for generating modulated waveforms because you are not constrained by the irregular timing associated with using the SPI registers.