NFA models with characters on nodes, not edges
Hyperscan chief architect here.

The buzzword you are looking for is a Glushkov NFA, as opposed to a Thompson NFA. 

The 'traditional model' you refer to is a Thompson NFA but is by no means the only choice. Both have their strengths and weaknesses, but we found the Glushkov NFA quite economical and it maps very nicely to a bitwise implementation (the "LimEx" NFA is a concrete NFA implementation, as opposed to the NFAGraph, which is an abstract representation). The joy of the Glushkov NFA is that the calculation of "reach" (which states are reached on which characters) and "succ" (which states can succeed other states) are completely independent and can be combined with a simple AND operation.

Gonzalo Navarro has a number of very nice papers and an excellent book on this subject. In terms of underlying approaches (if no the specific algorithms) we are entirely indebted to him.

Feel free to contact the Hyperscan list or alias if you want more information. We have been very lax in terms of writing up our approach.