AFAICT, this framework injects entropy directly into the underlying cryptographic primitive instead of treating the entropy collection/estimation and randomness extraction as two separate phases. Is my understanding correct?
Yes, that's my understanding as well.
What quantitative benefits does this framework have over the more traditional seed-based design?
The benefit is that if the entropy source is under partial control of an attacker it will still be possible to create a secure random number generator, assuming that enough entropy is left of course. If you assume that the entropy pool is not under control and delivers enough entropy to a traditional PRNG using the seed(s) then the benefits seem non-existent. Here's where I struggle a bit, because "partial control" seems to be tricky to accomplish.
In the traditional approach you could argue that the PRNG requires another PRNG-like construction (such as a KDF or, in the case of Intel, a PRF/MAC) to create the short, universally random bit string to be used as the seed.