I do not hold a PhD in astrophysics but if I read the article correctly the core issue is essentially the application of exotic "negative matter" (or energy), not be confused with "antimatter" or "dark matter" (quite a euphemism for something that actually is invisible and an issue even Professor Stephen Hawking seems to prefer to avoid
If I recall correctly the application of negative matter for spaceship propulsion is the brainchild of Professor Forward. Put at the end of a spaceship the negative matter's repelling effect suppossedly would propel the ship forward and also all the cosmic particles in front of it.
In contrast the Star Trek warp engines contract ("warp") the fabric of space to cut down interstellar length and travel.
According to Professor Hawking the biggest problem in the context for Star Trek would be that by changing the fabric of space you also change time. But then, according to "The Cage" they had possibly overcome difficulties of the "time warp barrier".
Sufficient to know it works very well - like the infamous Heisenberg compensators
. Just my 0.02 $