The shots definitely follow an arcing path towards their target. While we can understand why this was styled as such for out-of-universe reasons, I've yet to find any rational in-universe explaination for it that matches previous canon. That said, there are at least two possible reasons I can think of.
1) They may be near a gravity well of some sort
While the planet was obviously quite far away, I don't believe we ever see from space the star it orbits. It's possible it was "down" from our perspective in space even while unseen, which could explain the need to calculate an arc trajectory to compensate for gravity. A nearby black hole is likewise a possibility.
2) The shots themselves are capable of adjusting course
Similar to proton torpedos in A New Hope, but perhaps more akin to the Starkiller Base splitting beam, we've seen non-missle weapons capable of changing course mid-flight in canon. Considering the shots almost never seemed to miss, perhaps they were able to "lock on" or be drawn to the target regardless of firing angle, and the arc was intended to hit their shields from different sides to find a weakness. This wouldn't be too far fetched, considering all the new tech the First Order seems to have access to.
I admit both of these are unsubstantiated, and without more information there's no way to be certain. But until we're given more information, these are at least potential explainations for the behavior we see.