I prefer to call it "hyperscience", rather than "magic" - this is a sci-fi game, not a fantasy game. The difference between sci-fi and fantasy is that in sci-i. questions like "how do I get from here (21st century Earth) to there (the spacetime where the sci-fi story is set)" and "how does this thing work" are not only allowed, but encouraged and expected; in fantasy, you're supposed to switch off the rational part of your brain and not ask such questions.
First, it should be pointed out that there are two different faster-than-light technologies in the Elite universal canon. The older tech is "hyperspace", the newer tech is the FSD. Jaques station seems to have had an older-tech hyperdrive installed, not a frame shift drive (which apparently does not work well on larger vessels). That's why he was able to make a single long jump, much longer than the FSD-powered carriers and capital ships we have experience with. FSD jumps take just a few seconds; hyperspace takes days, weeks, even months to get where you want to go. FSD travel between star systems is sometimes, confusingly, called "hyper-jumping", but it actually has nothing to do with hyperspace.
As for the theory on "how it works":
Hyperspace - also called "witch space" in the Elite universe, perhaps due to early copyright concerns over the use of the word "hyperspace" - is a variant on the standard "transdimensional travel" trope commonly found in sci-fi stories (such as "Star Wars"). In some not-entirely-explainable-to-21st-century-people way, hyperspace is an alternate plane or set of dimensions. Travelling in hyperspace is not bound by real-space's petty rules about "don't travel faster than light". Or, in some explanations, hyperspace's dimensions are compressed, so that travelling just a short distance in hyperspace equates to a huge distance in the real-world universe. As always, the difficulty with using hyperspace to go fast is making the transition between dimensions - "punching through" to get into hyperspace, then punching back out again to arrive at the intended destination. It's that "punching" that requires vast amounts of energy, the actual travel requires very little by comparison.
In Elite lore, a human spaceship in hyperspace is indeed following a preset course. Thargoid ships were apparently capable of much more maneuverability in hyperspace, but Human ships were not - you either arrived at your destination, or you didn't. Hyperspace travel, however, was prone to "mis-jumps". A ship suffering a mis-jump is knocked out of hyperspace, often someplace quite far away from either the departure point or the intended arrival. Jaque was, apparently, aiming for Beagle point, so was presumably travelling in a straight-line to get there, but ended up several thousand light-years off to one side of the straight-line route.