The lesson we should really take here is the power of wishful thinking. People dearly want to believe in FTL travel. Without it, the Universe just seems so vast, empty and distant. The truth is it is and it isn't. It's only really that on our current time scales.
Not to be a broken record (there's some new variation on some old idea like every week it seems), but I'm firmly in the camp that believes FTL isn't possible. There are two prongs to that.
1. Theoretical: a lot of these theories rely on people not understanding the domain of a function (eg plugging in negative mass or energy into an equation; just because a function can operate over real numbers doesn't mean real numbers are the domain of that function); and
2. The macro evidence in that if FTL were possible it makes it that much more unlikely that we haven't detected starfaring life. Specifically, the potential volume of spacetime goes from a line cone of several million light years to the entire Universe (not just the observable Universe). We don't know how big that is of course but it's may orders of magnitude larger.
So this paper tries to "solve" the negative energy/mass problem. I honestly can't speak to the soundness of this idea. I am however skeptical.