If I had to guess, which I do, I'd say it's probably a voxel size constraint. As long as one voxel is bigger than a perceivable pixel, all you can really do is interpolate the GI values within the voxel grid. That's is why lights moving smoothly and linearly will look slightly "choppy". It's probably less obvious in most real-world applications.
Again, just a wild guess based on watching that clip, I'm open to corrections!
I suspect the global illumination is running at a lower refresh rate than the rest of the scene for performance. I've seen other Godot demos that don't have this jerkiness.
