I don't know how they plan to handle it. In a similar game I've worked on (unpublished) gravity is handled like our universe, but with a bias toward the three orthogonal axis. This leaves you feeling like a 2d world on the faces, but as you approach to edges you begin to lean into them until you are "standing on the peak of the roof" at the edge, continuing brings you upright on the next face. A coefficient governs the strength of the bias, which I adjusted to trade off the width of the "funny" zones and the gravity direction gradient.
At the center of the planets, there is a singularity (which if you screw up the math can catapult you into space, game debugging has lots of fun to it) but is actually a non-issue because the strength of the gravity approaches zero, so the fact that it flips around in directions doesn't really matter, after you debug it.
You could probably avoid bugs at the center of planets by simply having an small cube of unmineable material surrounding them (like minecraft's bedrock).
At the center of the planets, there is a singularity (which if you screw up the math can catapult you into space, game debugging has lots of fun to it) but is actually a non-issue because the strength of the gravity approaches zero, so the fact that it flips around in directions doesn't really matter, after you debug it.