So a lot of space-based games have point-and-go space travel, in which you just point your ship where you want to go and apply thrust, both within and without a solar system. This has been criticized as inaccurate, but at the speeds one is traveling in such games (including this one) it's actually closer to what would happen.

Yes, real-world space probes use complex orbital maneuvers in which the effects of various gravitational fields predominate to reduce the thrust required. This is necessary because these probes can't get going much faster than the inner planets go around the Sun (<100 km/s), as they use chemical propellants with specific impulse <1000 seconds. (Ion thrusters get much better specific impulse, but their thrust at any one time is limited because of power requirement.) However, in-game, the speed indicator generally shows you traveling at a handful of AU per hour. As an AU is the distance between Earth and Sol, a velocity of 1 AU/hr is equivalent to about 42,000 km/s, or about 14% of the *speed of light*. And no, this isn't just an issue with the flavor text: according to the in-game calendar, you're crossing solar systems in a matter of days, which is consistent with this. Evidently, the main engine is an antimatter drive, as achieving these kinds of velocities in such a brief period is not possible any other way (not being crushed by the acceleration is evidently handled by the artificial gravity system). (There would also be significant time dilation and Doppler effect at these speeds, but let's not go there.)

This is relevant in that hyperbolic trajectories at this speed would be nearly straight lines. The speeds are hundreds of times greater than those of planets about the Sun (or other stars): the gravity of stars and planets would exert a negligible change in such velocities. Point-and-go actually is accurate for such advanced propulsion systems.

I don't want or expect them to change the game (though it's worth noting that IRL, trajectories like this can be plotted out in detail beforehand, and don't have to be worked out on the fly based on a projection that cuts off at the edge of a bounded window). However, for those interested in how this stuff actually works, it's worth understanding how these kinds of trajectories are (with present technology) and are not (with futuristic propulsion systems) accurate.