Read the HP Journal April 1971.
The analog output is generated by summing binary digital outputs. Each binary is weighted (gain) with a resistor. It is a non-linear DAC.
In a DSP you could achieve the same by ANDing the binaries with numbers (gain), then summing to produce a single output value. Apply this to the DAC.
This approach gives the option of staying digital, or going analogue.
This clarifies the functionality of the LFSR but doesn’t address the rationale for placing a DAC between the LFSR and the output.
Do I understand correctly that the DAC is intended to act as a filter to shape the flat noise response of the LFSR into a specific curve?
What specific frequency response are you aiming to achieve using the DAC as a filter?
For example, here is the spectrum of digital noise (direct output from LFSR):

And here is the spectrum of analog noise (using DAC between LFSR and output):

I don't see significant difference, except a little ~3 dB noise power offset. So, I'm trying to understand the reason to use DAC for noise generator...