(I'm not an expert)

I think the HTK doesn't use neural networks at all. What it does is simply computes the MFCC of the sound signal and use it as input to a chain of HMM models. Well, "simply" that, plus the dozens of refinements and tweakings to make that work well.

Here, I guess they do some sort of preprocessing on the sounds features using their deep neural networks before feeding the whole thing to the HMMs.