I suspect that as we can’t even work out how to stop over-fishing the oceans and over-heating our planet, it’s a bit moot to speculate about quasi-fictional drives. But here are a few issues:
First of all, the notion behind “warping space” doesn’t take into account quantum vacuum effects at all, and these are likely to turn out to be very important. Remember: we don’t yet have a proper quantum field theory for gravity but we do know that effects at the Planck scale have significant impact on supposedly “empty” space and the quantum tensor fields therein. Which could cause serious problems for any attempt to warp space in a purposeful manner.
Secondly, unless we only want to move a few millimeters, we’d need to do a great deal of warping. Even super-massive black holes don’t actually warp space to the degree necessary to accomplish movement over significant distances. This in turn implies that the energy calculations aren’t very realistic (and even so, how exactly are we supposed to engineer conversion of Jupiter into usable power for a small vehicle…?).
Finally, there’s no mention of how we’d isolate the ship (and its occupants) from the astonishing forces required to warp spacetime to the degree envisaged.
NASA has a long history of investigating silly ideas, the most recent being the supposed motor that generated magic thrust by means of an asymmetric chamber (but was really just a poorly-designed piece of equipment with unshielded wires). So the fact that someone in NASA is willing to glance at a speculative paper isn’t really much of an endorsement and shouldn’t be taken to indicate anything meaningful at all.