A few takeaways; they intend for such an engine to eventually support long duration human spaceflight (going to Mars.) The propellant for the NTR engine to be liquid hydrogen. One of the problems DARPA anticipates with using such an engine for such a mission is needing to store liquid hydrogen longer than the present state of the art.
The PDF doesn't seem to mention it, but I think the Advanced Cryogenic Evolved Stage (ACES) is probably relevant to this project. Does anybody know what kind of duration they expect to get from ACES? I'm not sure but I think it's weeks, not months.