I'm not an astrophysicist or warp theorist so keep that in mind as I attempt to answer the question. 

The basic engine you start with in the game is a String Gravitics engine which would suggest the game's universe is built upon the String Theory of quantum gravity. In this theory, matter and radiation are composed of one-dimensional objects called strings as opposed to zero-dimensional objects called point-particles. This theoretical construction of the universe creates a framework for the physics of the universe in which travel via the manipulation of gravitons, the quantum of gravity, along congregated strings in the universe is possible. This would create a theoretical "star lane" as used by the game. 

To put it as simply as possible, the idea is that a collection of the smallest measurable forces of gravity have grouped together in such a way as to allow an object (in this case a ship) to use the gravity field generated by this as a form of populsion up and down the field, like a "road" in space. 

The premise behind a "warp engine" in this situation would be an engine that is capable of generating its own gravity field around a ship and then manipulate it in such a way as to interact with the gravitons of strings surrounding the vessel to create propulsion without the need for a congregated body of them, thus freeing the vessel to move about as needed rather than being limited to the "road" created as described above. 

Also, I belive the "Celestial Vines" of the Unfallen are in-fact generated by Dust but are more akin to a spider's web or very thin strings woven together to create a "vine" that would be largely imperceptbile to the naked eye and thus not the "space load of Dust" that HuskOfKnowledge describes because yeah, if vines were constructed of Dust and were of any measurable mass then the Unfallen would be generating Dust for everyone else to harvest at will.